Abstract
In the introduction to this volume, we discuss some of the highlights of the research career of Chuck Newman. This introduction is divided into two main sections, the first covering Chuck’s work in statistical mechanics and the second his work in percolation theory, continuum scaling limits, and related topics.
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References
Aizenman, M.: Scaling limit for the incipient spanning clusters. In: Mathematics of Multiscale Materials, pp. 1–24. Springer, New York (1998)
Aizenman, M., Barsky, D.J.: Sharpness of the phase transition in percolation models. Commun. Math. Phys. 108(3), 489–526 (1987)
Aizenman, M., Burchard, A.: Hölder regularity and dimension bounds for random curves. Duke Math. J. 99(3), 419–453 (1999)
Aizenman, M., Burchard, A., Newman, C.M., Wilson, D.B.: Scaling limits for minimal and random spanning trees in two dimensions. Random Struct. Algorithms 15(3–4), 319–367 (1999)
Aizenman, M., Chayes, J.T., Chayes, L., Newman, C.M.: Discontinuity of the magnetization in one-dimensional \(1/|x-y|^2\) Ising and Potts models. J. Stat. Phys. 50, 1–40 (1988)
Aizenman, M., Fisher, D.S.: Unpublished
Aizenman, M., Kesten, H., Newman, C.M.: Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation. Commun. Math. Phys. 111(4), 505–531 (1987)
Aizenman, M., Newman, C.M.: Tree graph inequalities and critical behavior in percolation models. J. Stat. Phys. 36(1), 107–143 (1984)
Aizenman, M., Newman, C.M.: Discontinuity of the percolation density in one dimensional \(1/|x-y|^2\) percolation models. Commun. Math. Phys. 107(4), 611–647 (1986)
Aizenman, M., Wehr, J.: Rounding effects of quenched randomness on first-order phase transitions. Commun. Math. Phys. 130, 489–528 (1990)
Arguin, L.P., Damron, M., Newman, C.M., Stein, D.L.: Uniqueness of ground states for short-range spin glasses in the half-plane. Commun. Math. Phys. 300, 641–657 (2010)
Arguin, L.P., Newman, C.M., Stein, D.L.: Thermodynamic identities and symmetry breaking in short-range spin glasses. Phys. Rev. Lett. 115, 187–202 (2015)
Arguin, L.P., Newman, C.M., Stein, D.L., Wehr, J.: Fluctuation bounds for interface free energies in spin glasses. J. Stat. Phys. 156, 221–238 (2014)
Arguin, L.P., Newman, C.M., Stein, D.L., Wehr, J.: Fluctuation bounds in spin glasses at zero temperature. J. Stat. Phys. 165, 1069–1078 (2016)
Arous, G.B., Cerný, J.: Dynamics of trap models. In: Mathematical Statistical Physics Lecture Notes, vol. LXXXIII, Les Houches Summer School, pp. 331–394. North-Holland, Amsterdam (2006)
Arratia, R.: Coalescing Brownian motions on the line. Ph.D. Thesis, Univ. Wisconsin, Madison (1979)
Arratia, R.: Coalescing Brownian motions and the voter model on \(F\) (1981). Unpiblished manuscript
Aspelmeier, T., Katzgraber, H.G., Larson, D., Moore, M.A., Wittmann, M., Yeo, J.: Finite-size critical scaling in Ising spin glasses in the mean-field regime. Phys. Rev. E 93, 032123 (2016)
Auffinger, A., Damron, M.: Differentiability at the edge of the percolation cone and related results in first-passage percolation. Probab. Theory Relat. Fields 156(1), 193–227 (2013)
Auffinger, A., Damron, M., Hanson, J.: 50 Years of First-Passage Percolation. American Mathematical Society, Providence (2017)
Badoni, D., Ciria, J., Parisi, G., Ritort, F., Pech, J., Ruiz-Lorenzo, J.: Numerical evidence of a critical line in the \(4d\) Ising spin glass. Europhys. Lett. 21, 495–499 (1993)
Ballesteros, H., Cruz, A., Fernández, L., Martin-Mayor, V., Pech, J., Ruiz-Lorenzo, J., Tarancón, A., Téllez, P., Ullod, C., Ungil, C.: Critical behavior of the three-dimensional Ising spin glass. Phys. Rev. B 62, 14237 (2000)
Banavar, J.R., Cieplak, M., Maritan, A.: Optimal paths and domain walls in the strong disorder limit. Phys. Rev. Lett. 72, 2320–2323 (1994)
Barsky, D., Aizenman, M.: Percolation critical exponents under the triangle condition. Ann. Probab. 19, 1520–1536 (1991)
Barsky, D.J., Grimmett, G.R., Newman, C.M.: Percolation in half-spaces: equality of critical densities and continuity of the percolation probability. Probab. Theory Relat. Fields 90(1), 111–148 (1991)
Barsky, D.J., Wu, C.C.: Critical exponents for the contact process under the triangle condition. J. Stat. Phys. 91(1), 95–124 (1998)
Beffara, V., Nolin, P.: On monochromatic arm exponents for 2D critical percolation. Ann. Probab. 39(4), 1286–1304 (2011)
Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Infinite conformal symmetry in two-dimensional quantum field theory. Nucl. Phys. B 241(2), 333–380 (1984)
Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Infinite conformal symmetry of critical fluctuations in two dimensions. J. Stat. Phys. 34(5), 763–774 (1984)
Benjamini, I., Schramm, O.: Percolation beyond , many questions and a few answers. Electron. Commun. Probab. 1, 71–82 (1996)
Bethe, H.: Statistical theory of superlattices. Proc. Roy. Soc. London A: Math. Phys. Eng. Sci. 150(871), 552–575 (1935)
Billoire, A., Maiorano, A., Marinari, E., Martin-Mayor, V., Yllanes, D.: Cumulative overlap distribution function in realistic spin glasses. Phys. Rev. B 90, 094201 (2014)
Binder, K., Young, A.P.: Spin glasses: experimental facts, theoretical concepts, and open questions. Rev. Mod. Phys. 58, 801–976 (1986)
Bleher, P.M., Sinai, J.G.: Investigation of the critical point in models of the type of dyson’s hierarchical models. Commun. Math. Phys. 33(1), 23–42 (1973)
Bokil, H., Bray, A.J., Drossel, B., Moore, M.A.: Comment on ‘General method to determine replica symmetry breaking transitions’. Phys. Rev. Lett. 82, 5174 (1999)
Bokil, H., Drossel, B., Moore, M.A.: The influence of critical behavior on the spin glass phase (2000). Available as cond-mat/0002130
Bollobas, B., Riordan, O.: Percolation. Cambridge University Press, New York (2006)
Borgs, C., Chayes, J.T., van der Hofstad, R., Slade, G., Spencer, J.: Random subgraphs of finite graphs. II. The lace expansion and the triangle condition. Ann. Probab. 33(5), 1886–1944 (2005)
Borthwick, D., Garibaldi, S.: Did a 1-dimensional magnet detect a 248-dimensional Lie algebra? Notices Amer. Math. Soc. 58, 1055–1066 (2011)
Bouchaud, J.P.: Weak ergodicity breaking and aging in disordered systems. J. Phys. I(2), 1705–1713 (1992)
Bray, A.J., Moore, M.A.: Critical behavior of the three-dimensional Ising spin glass. Phys. Rev. B 31, 631–633 (1985)
Bray, A.J., Moore, M.A.: Chaotic nature of the spin-glass phase. Phys. Rev. Lett. 58, 57–60 (1987)
Broadbent, S.: Contribution to discussion on symposium on Monte Carlo methods. J. Roy. Statist. Soc. B 16, 68 (1954)
Broadbent, S.R., Hammersley, J.M.: Percolation processes: I. Crystals and mazes. In: Mathematical Proceedings of the Cambridge Philosophical Society, 53(3), pp. 629–641 (1957)
Bruijn, N.G.D.: The roots of trigonometric integrals. Duke Math. J. 17, 197–226 (1950)
Burton, R.M., Keane, M.: Density and uniqueness in percolation. Commun. Math. Phys. 121(3), 501–505 (1989)
Burton, R.M., Keane, M.: Topological and metric properties of infinite clusters in stationary two-dimensional site percolation. Isr. J. Math. 76, 299–316 (1991)
Cacciuto, A., Marinari, E., Parisi, G.: A numerical study of ultrametricity in finite-dimensional spin glasses. J. Phys. A 30, L263–L269 (1997)
Camia, F., Fontes, L.R.G., Newman, C.M.: The scaling limit geometry of near-critical 2D percolation. J. Stat. Phys. 125, 57–69 (2006)
Camia, F., Fontes, L.R.G., Newman, C.M.: Two-dimensional scaling limits via marked nonsimple loops. Bull. Braz. Math. Soc. 37(4), 537–559 (2006)
Camia, F., Garban, C., Newman, C.M.: The Ising magnetization exponent on \(\mathbb{Z}^2\) is \(1/15\). Probab. Theory Rel. Fields 160, 175–187 (2014)
Camia, F., Garban, C., Newman, C.M.: Planar Ising magnetization field I. Uniqueness of the critical scaling limits. Ann. Probab. 43, 528–571 (2015)
Camia, F., Garban, C., Newman, C.M.: Planar Ising magnetization field II. Properties of the critical and near-critical scaling limits. Ann. Inst. H. Poincaré Probab. Statist. 52, 146–161 (2016)
Camia, F., Jiang, J., Newman, C.M.: Exponential decay for the near-critical scaling limit of the planar Ising model. Commun. Pure Appl. Math. (2017, to appear). arXiv:1707.02668
Camia, F., Jiang, J., Newman, C.M.: New FK–Ising coupling applied to near-critical planar models. arXiv:1709.00582
Camia, F., Joosten, M., Meester, R.: Trivial, critical and near-critical scaling limits of two-dimensional percolation. J. Stat. Phys. 137, 57–69 (2009)
Camia, F., Newman, C.M.: Continuum nonsimple loops and 2D critical percolation. J. Stat. Phys. 116(1), 157–173 (2004)
Camia, F., Newman, C.M.: The full scaling limit of two-dimensional critical percolation (2005). arXiv:math.PR/0504036
Camia, F., Newman, C.M.: Two-dimensional critical percolation: the full scaling limit. Commun. Math. Phys. 268(1), 1–38 (2006)
Camia, F., Newman, C.M.: Critical percolation exploration path and \(SLE_6\): a proof of convergence. Probab. Theory Relat. Fields 139(3), 473–519 (2007)
Camia, F., Newman, C.: SLE6 and CLE6 from critical percolation. In: Pinsky, M., Birnir, B. (eds.) Probability, Geometry and Integrable Systems, Mathematical Sciences Research Institute Publications 55, vol. 55, pp. 103–130. Cambridge University Press, Cambridge (2008)
Camia, F., Newman, C.M.: Ising (conformal) fields and cluster area measures. Proc. Natl. Acad. Sci. (USA) 14, 5457–5463 (2009)
Caracciolo, S., Parisi, G., Patarnello, S., Sourlas, N.: Low temperature behaviour of 3-\({D}\) spin glasses in a magnetic field. J. Phys. France 51, 1877–1895 (1990)
Cator, E., Pimentel, L.P.R.: A shape theorem and semi-infinite geodesics for the Hammersley model with random weights. LEA: Lat. Am. J. Probab. Math. Stat. 8, 163–175 (2011)
Chatterjee, S.: Disorder chaos and multiple valleys in spin glasses (2009). arXiv:0907.3381
Chatterjee, S.: The universal relation between scaling exponents in first-passage percolation. Ann. Math. 177(2), 663–697 (2013)
Chayes, J., Chayes, L.: An inequality for the infinite cluster density in Bernoulli percolation. Phys. Rev. Lett. 56, 1619–1622 (1986)
Chelkak, D., Hongler, C., Izyurov, K.: Conformal invariance of spin correlations in the planar Ising model. Ann. Math. 181, 1087–1138 (2015)
Borgs, C., Chayes, J.T., van der Hofstad, R., Slade, G., Spencer, J.: Random subgraphs of finite graphs: I. The scaling window under the triangle condition. Random Struct. Algorithms 27(2), 137–184 (2005)
Cohen, J.E., Newman, C.M., Briand, F.: A stochastic theory of community food webs: II. Individual webs. Proc. Royal Soc. London B224, 449–461 (1985)
Contucci, P., Giardiná, C., Giberti, C., Parisi, G., Vernia, C.: Ultrametricity in the Edwards-Anderson model. Phys. Rev. Lett. 99, 057206 (2007)
Cox, J.T., Durrett, R.: Some limit theorems for percolation processes with necessary and sufficient conditions. Ann. Probab. 9(4), 583–603 (1981)
Damron, M., Hanson, J.: Bigeodesics in first-passage percolation. Commun. Math. Phys. 349(2), 753–776 (2017)
Damron, M., Hochman, M.: Examples of nonpolygonal limit shapes in I.I.D. First-passage percolation and infinite coexistence in spatial growth models. Ann. Appl. Probab. 23(3), 1074–1085 (2013)
Delfino, G.: Integrable field theory and critical phenomena: the Ising model in a magnetic field. J. Phys. A: Math. Gen. 37, R45–R78 (2004)
Derrida, B., Toulouse, G.: Sample to sample fluctuations in the random energy model. J. Phys. (Paris) Lett. 46, L223–L228 (1985)
Doyon, B.: Calculus on manifolds of conformal maps and CFT. J. Phys. A: Math. Theor. 45, 315202 (2012)
Doyon, B.: Conformal loop ensembles and the stress-energy tensor. Lett. Math. Phys. 103, 233–284 (2013)
Doyon, B.: Random loops and conformal field theory. J. Stat. Mech. Ther. Expt. 46, 46039207 (2014)
Drossel, B., Bokil, H., Moore, M.A., Bray, A.J.: The link overlap and finite size effects for the \(3{D}\) Ising spin glass. Eur. Phys. J. B 13, 369–375 (2000)
Dubédat, J.: Excursion decompositions for SLE and Watts’ crossing formula. Probab. Theory Relat. Fields 134(3), 453–488 (2006)
Dubédat, J.: Exact bosonization of the Ising model (2011). arXiv:1112.4399
Dunlop, F.: Zeros of the partition function and Gaussian inequalities for the plane rotator model. J. Stat. Phys. 21, 561–572 (1979)
Dunlop, F., Newman, C.M.: Multicomponent field theories and classical rotators. Commun. Math. Phys. 44, 223–235 (1975)
Dyson, F.: General theory of spin-wave interactions. Phys. Rev. 102, 1217–1229 (1956)
Dyson, F.J.: Existence of a phase-transition in a one-dimensional Ising ferromagnet. Commun. Math. Phys. 12(2), 91–107 (1969)
Edwards, R.G., Sokal, A.D.: Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm. Phys. Rev. D 38, 2009–2012 (1988)
Edwards, S., Anderson, P.W.: Theory of spin glasses. J. Phys. F 5, 965–974 (1975)
Ellis, R.S., Newman, C.M.: Limit theorems for sums of dependent random variables occurring in statistical mechanics. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 44(2), 117–139 (1978)
Ellis, R.S., Newman, C.M.: The statistics of Curie-Weiss models. J. Stat. Phys. 19(2), 149–161 (1978)
Ellis, R.S., Newman, C.M., Rosen, J.S.: Limit theorems for sums of dependent random variables occurring in statistical mechanics. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 51(2), 153–169 (1980)
Fernandez, R., Fröhlich, J., Sokal, A.D.: Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory. Springer, Berlin (1992)
Ferrari, P.A., Pimentel, L.P.R.: Competition interfaces and second class particles. Ann. Probab. 33(4), 1235–1254 (2005)
Fisher, D.S., Huse, D.A.: Ordered phase of short-range Ising spin-glasses. Phys. Rev. Lett. 56, 1601–1604 (1986)
Fisher, D.S., Huse, D.A.: Absence of many states in realistic spin glasses. J. Phys. A 20, L1005–L1010 (1987)
Fisher, D.S., Huse, D.A.: Pure States in Spin Glasses. J. Phys. A 20, L997–L1004 (1987)
Fisher, D.S., Huse, D.A.: Equilibrium behavior of the spin-glass ordered phase. Phys. Rev. B 38, 386–411 (1988)
Fisher, D.S., Huse, D.A.: Nonequilibrium dynamics of spin glasses. Phys. Rev. B 38, 373–385 (1988)
Fitzner, R., van den Hofstad, R.: Nearest-neighbor percolation function is continuous for \(d > 10\): extended version (2015). arXiv:1506.07977
Fontes, L.R.G., Isopi, M., Newman, C.M.: Chaotic time dependence in a disordered spin system. Prob. Theory Rel. Fields 115, 417–433 (1999)
Fontes, L.R.G., Isopi, M., Newman, C.M.: Random walks with strongly inhomogeneous rates and singular diffusions: convergence, localization and aging in one dimension. Ann. Probab. 30, 579–604 (2002)
Fontes, L.R.G., Isopi, M., Newman, C.M., Ravishankar, K.: The Brownian web: characterization and convergence. Ann. Probab. 32(4), 2857–2883 (2004)
Fontes, L.R.G., Isopi, M., Newman, C.M., Stein, D.L.: Aging in \(1{D}\) discrete spin models and equivalent systems. Phys. Rev. Lett. 87, 1102011 (2001)
Fontes, L.R., Isopi, M., Newman, C.M., Ravishankar, K.: The Brownian web. Proc. Natl. Acad. Sci. 99, 15888–15893 (2002)
Forgacs, G., Lipowsky, R., Nieuwenhuizen, T.M.: The behavior of interfaces in ordered and disordered systems. In: Domb, C., Lebowitz, J. (eds.) Phase Transitions and Critical Phenomena, vol. 14, pp. 135–363. Academic Press, London (1991)
Fortuin, C.M., Kasteleyn, P.W.: On the random-cluster model. I. Introduction and relation to other models. Physica 57, 536–564 (1972)
Francesco, P., Mathieu, P., Senechal, D.: Conformal Field Theory. Graduate Texts in Contemporary Physics, corrected edn. Springer, New York (1997)
Fröhlich, J., Rodriguez, P.F.: Some applications of the Lee-Yang theorem. J. Math. Phys. 53, 095218 (2012)
Fröhlich, J., Spencer, T.: On the statistical mechanics of classical Coulomb and dipole gases. J. Stat. Phys. 24, 617–701 (1981)
Gandolfi, A., Keane, M., Newman, C.M.: Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses. Probab. Theory Relat. Fields 92, 511–527 (1992)
Garban, C., Pete, G., Schramm, O.: Pivotal, cluster, and interface measures for critical planar percolation. J. Amer. Math. Soc. 26, 939–1024 (2013)
Garet, O., Marchand, R.: Moderate deviations for the chemical distance in Bernoulli percolation. ALEA: Lat. Am. J. Probab. Math. Stat. 7, 171–191 (2010)
Glimm, J., Jaffe, A.: Quantum Physics: A Functional Integral Point of View, 2nd edn. Springer, Berlin (1987)
Grimmett, G.: The random-cluster model. Grundlehren der mathematischen Wissenschaften 333, (2016)
Grimmett, G.R.: Percolation. Springer, Berlin (1999)
Guerra, F., Rosen, L., Simon, B.: Correlation inequalities and the mass gap in \(p(\phi )_2\). Commun. Math. Phys. 41, 19–32 (1975)
Guggenheim, E.A.: The principle of corresponding states. J. Chem. Phys. 13(7), 253–261 (1945)
Gunnarson, K., Svedlindh, P., Nordblad, P., Lundgren, L., Aruga, H., Ito, A.: Static scaling in a short-range Ising spin glass. Phys. Rev. B 43, 8199 (1991)
Hammersley, J.M.: Percolation processes: lower bounds for the critical probability. Ann. Math. Stat. 28(3), 790–795 (1957)
Hammersley, J.M.: Bornes supérieures de la probabilité critique dans un processus de filtration. In: Le Calcul des Probabilités et ses Applications. Paris, 15-20 Juillet 1958, p. 790–795. Centre National de la Recherche Scientifique (1959)
Hammersley, J.M., Welsh, D.J.A.: First-Passage Percolation, Subadditive Processes, Stochastic Networks, and Generalized Renewal Theory, pp. 61–110. Springer, Heidelberg (1965)
Hara, T., Slade, G.: The triangle condition for percolation. Bull. Am. Math. Soc. (N.S.) 21, 269–273 (1989)
Hara, T., Slade, G.: Mean-field critical behaviour for percolation in high dimensions. Commun. Math. Phys. 128(2), 333–391 (1990)
Hasenbusch, M., Pelissetto, A., Vicari, E.: Critical behavior of three-dimensional Ising spin glass models. Phys. Rev. B 78, 214205 (2008)
Hed, G., Young, A.P., Domany, E.: Lack of ultrametricity in the low-temperature phase of three-dimensional Ising spin glasses. Phys. Rev. Lett. 92, 157201 (2004)
Hoffman, C.: Geodesics in first passage percolation. Ann. Appl. Probab. 18(5), 1944–1969 (2008)
Hongler, C.: Conformal invariance of Ising model correlations. Ph.D. dissertation, Univ. Geneva (2010)
Hongler, C., Smirnov, S.: The energy density in the planar Ising model. Acta Math. 211, 191–225 (2013)
Howard, C.D., Newman, C.M.: Euclidean models of first-passage percolation. Probab. Theory Relat. Fields 108(2), 153–170 (1997)
Howard, C.D., Newman, C.M.: From Greedy Lattice Animals to Euclidean First-Passage Percolation, pp. 107–119. Birkhäuser Boston, Boston (1999)
Howard, C.D., Newman, C.M.: Geodesics and spanning trees for Euclidean first-passage percolation. Ann. Probab. 29(2), 577–623 (2001)
Ising, E.: Beitrag zur theorie des ferromagnetismus. Z. Phys. 31, 253–258 (1925)
Jackson, T.S., Read, N.: Theory of minimum spanning trees. I. Mean-field theory and strongly disordered spin-glass model. Phys. Rev. E 81, 021130 (2010)
Baity-Jesi, M., et al.: (Janus Collaboration): Critical parameters of the three-dimensional Ising spin glass. Phys. Rev. B 88, 224416 (2013)
Jona-Lasinio, G.: The renormalization group: a probabilistic view. Il Nuovo Cimento B (1971–1996) 26(1), 99–119 (1975)
Jona-Lasinio, G.: Probabilistic Approach to Critical Behavior, pp. 419–446. Springer, Boston (1977)
Jona-Lasinio, G.: Renormalization group and probability theory. Phys. Rep. 352(4), 439–458 (2001). Renormalization group theory in the new millennium. III
Kasteleyn, P.W., Fortuin, C.M.: Phase transitions in lattice systems with random local properties. J. Phys. Soc. Jpn. [Suppl.] 26, 11–14 (1969)
Katzgraber, H.G., Krzakala, F.: Temperature and disorder chaos in three-dimensional Ising spin glasses. Phys. Rev. Lett. 98, 017201 (2007)
Katzgraber, H.G., Palassini, M., Young, A.P.: Monte Carlo simulations of spin glasses at low temperatures. Phys. Rev. B 63, 184422 (2001)
Katzgraber, H.G., Young, A.P.: Probing the Almeida-Thouless line away from the mean-field model. Phys. Rev. B 72, 184416 (2005)
Kemppainen, A., Werner, W.: The nested simple conformal loop ensembles in the Riemann sphere. Probab. Theory Relat. Fields 165, 835–866 (2016)
Kesten, H.: The critical probability of bond percolation on the square lattice equals \(1/2\). Commun. Math. Phys. 74(1), 41–59 (1980)
Kesten, H.: Percolation Theory for Mathematicians. Birkhauser, Boston (1982)
Kesten, H.: Aspects of First-Passage Percolation, pp. 125–264. Springer, Berlin (1986)
Kesten, H.: On the speed of convergence in first-passage percolation. Ann. Appl. Probab. 3, 296–338 (1993)
Ki, H., Kim, Y.O., Lee, J.: On the de Bruijn-Newman constant. Adv. Math. 222, 281–306 (2009)
Kipnis, C., Newman, C.M.: The metastable behavior of infrequently observed, weakly random, one-dimensional diffusion processes. SIAM J. Appl. Math. 45, 972–982 (1985)
Knauf, A.: Number theory, dynamical systems and statistical mechanics. Rev. Math. Phys. 11, 1027–1060 (1999)
Krug, J., Spohn, H.: Kinetic Roughening of Growing Interfaces, pp. 479–582. Cambridge University Press, Cambridge (1991)
Krzakala, F., Martin, O.C.: Spin and link overlaps in three-dimensional spin glasses. Phys. Rev. Lett. 85, 3013–3016 (2000)
Külske, C.: Limiting behavior in random Gibbs measures: metastates in some disordered mean field models. In: Bovier, A., Picco, P. (eds.) Mathematics of Spin Glasses and Neural Networks, pp. 151–160. Birkhauser, Boston (1998)
Külske, C.: Metastates in disordered mean-field models II: The superstates. J. Stat. Phys. 91, 155–176 (1998)
Landau, L.D.: On the theory of phase transitions. Zh. Eksp. Teor. Fiz. 7, 19–32 (1937). [Ukr. J. Phys.53,25(2008)]
Lawler, G.F., Schramm, O., Werner, W.: The dimension of the planar Brownian frontier is \(4/3\). Math. Res. Lett. 8, 401–411 (2001)
Lawler, G.F., Schramm, O., Werner, W.: Values of Brownian intersection exponents, I: Half-plane exponents. Acta Math. 187(2), 237–273 (2001)
Lawler, G.F., Schramm, O., Werner, W.: One-arm exponent for critical 2d percolation. Electron. J. Probab. 7, 13 pp. (2002)
Lawler, G.F., Schramm, O., Werner, W.: Conformal invariance of planar loop-erased random walks and uniform spanning trees. Ann. Probab. 32(1B), 939–995 (2004)
Lee, T.D., Yang, C.N.: Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model. Phys. Rev. 87, 410–419 (1952)
Lenz, W.: Beitrag zum Verständnis der magnetischen Erscheinungen in festen Körpern. Physik Zeitschr. 21, 613–615 (1920)
Licea, C., Newman, C., Piza, M.: Superdiffusivity in first-passage percolation. Probab. Theory Relat. Fields 106(4), 559–591 (1996)
Licea, C., Newman, C.M.: Geodesics in two-dimensional first-passage percolation. Ann. Probab. 24(1), 399–410 (1996)
Lieb, E.H., Sokal, A.D.: A general Lee-Yang theorem for one-component and multicomponent ferromagnets. Commun. Math. Phys. 80, 153–179 (1981)
Lyons, R.: Phase transitions on nonamenable graphs. J. Math. Phys. 41(3), 1099–1126 (2000)
Machta, J., Newman, C.M., Stein, D.L.: The percolation signature of the spin glass transition. J. Stat. Phys. 130, 113–128 (2008)
Machta, J., Newman, C.M., Stein, D.L.: Percolation in the Sherrington–Kirkpatrick spin glass. In: Sidoravicious, V., Vares, M.E. (eds.) Progress in Probability, vol. 60: In and Out of Equilibrium II, pp. 527–542. Birkhauser, Boston (2009)
Machta, J., Newman, C.M., Stein, D.L.: A percolation-theoretic approach to spin glass phase transitions. In: de Monvel, A.B., Bovier, A. (eds.) Proceedings of the 2007 Paris Spin Glass Summer School, Progress in Probability Series, vol. 62, pp. 205–223. Birkhauser, Boston (2009)
Marinari, E., Parisi, G.: Effects of changing the boundary conditions on the ground state of Ising spin glasses. Phys. Rev. B 62, 11677–11685 (2000)
Marinari, E., Parisi, G.: Effects of a bulk perturbation on the ground state of \(3{D}\) Ising spin glasses. Phys. Rev. Lett. 86, 3887–3890 (2001)
Marinari, E., Parisi, G., Ricci-Tersenghi, F., Ruiz-Lorenzo, J.J., Zuliani, F.: Replica symmetry breaking in spin glasses: theoretical foundations and numerical evidences. J. Stat. Phys. 98, 973–1047 (2000)
Marinari, E., Parisi, G., Ritort, F.: On the \(3{D}\) Ising spin glass. J. Phys. A 27, 2687–2708 (1994)
Marinari, E., Parisi, G., Ruiz-Lorenzo, J.: Numerical simulations of spin glass systems. In: Young, A.P. (ed.) Spin Glasses and Random Fields, pp. 59–98. World Scientific, Singapore (1997)
Marinari, E., Parisi, G., Ruiz-Lorenzo, J.J., Ritort, F.: Numerical evidence for spontaneously broken replica symmetry in \(3{D}\) spin glasses. Phys. Rev. Lett. 76, 843–846 (1996)
McCoy, B., Mallard, J.M.: The importance of the Ising model. Program. Theor. Phys. 127, 791–817 (2012)
McMillan, W.L.: Scaling theory of Ising spin glasses. J. Phys. C 17, 3179–3187 (1984)
Mermin, N.D., Wagner, H.: Absence of ferromagnetism or antiferromagnetism in one-or two-dimensional isotropic Heisenberg models. Phys. Rev. Lett. 17, 1133–1136 (1966)
Mézard, M., Parisi, G., Sourlas, N., Toulouse, G., Virasoro, M.: Nature of spin-glass phase. Phys. Rev. Lett. 52, 1156–1159 (1984)
Mézard, M., Parisi, G., Sourlas, N., Toulouse, G., Virasoro, M.: Replica symmetry breaking and the nature of the spin-glass phase. J. Phys. (Paris) 45, 843–854 (1984)
Mézard, M., Parisi, G., Virasoro, M.A.: Random free energies in spin glasses. J. Phys. (Paris) Lett. 46, L217–L222 (1985)
Mézard, M., Parisi, G., Virasoro, M.A. (eds.): Spin Glass Theory and Beyond. World Scientific, Singapore (1987)
Middleton, A.A.: Numerical investigation of the thermodynamic limit for ground states in models with quenched disorder. Phys. Rev. Lett. 83, 1672–1675 (1999)
Middleton, A.A.: Energetics and geometry of excitations in random systems. Phys. Rev. B 63, 060202 (2000)
Middleton, A.A.: Extracting thermodynamic behavior of spin glasses from the overlap function. Phys. Rev. B 87, 220201 (2013)
Miller, J., Sheffield, S., Werner, W.: CLE precolations. Forum Math. 5, 102 pages (2017)
Miller, J., Sun, N., Wilson, D.B.: The Hausdorff dimension of the CLE gasket. Ann. Probab. 42, 1644–1665 (2014)
Miller, J., Watson, S.S., Wilson, D.B.: The conformal loop ensemble nesting field. Probab. Theory Relat. Fields 163, 769–801 (2015)
Miller, J., Watson, S.S., Wilson, D.B.: Extreme nesting in the conformal loop ensemble. Ann. Probab. 44, 1013–1052 (2016)
Miller, J., Werner, W.: Connection probabilities for conformal loop ensembles. Commun. Math. Phys. 362, 415–453 (2018)
Moore, M.A., Bokil, H., Drossel, B.: Evidence for the droplet picture of spin glasses. Phys. Rev. Lett. 81, 4252–4255 (1998)
Nanda, S., Newman, C.M., Stein, D.L.: Dynamics of Ising spin systems at zero temperature. In: R. Minlos, S. Shlosman, Y. Suhov (eds.) On Dobrushin’s Way (from Probability Theory to Statistical Physics), pp. 183–194. Amer. Math. Soc. Transl. (2) 198 (2000)
Newman, C.M.: Ultralocal quantum field theory in terms of currents. Commun. Math. Phys. 26(3), 169–204 (1972)
Newman, C.M.: The construction of stationary two-dimensional Markoff fields with an application to quantum field theory. J. Funct. Anal. 14(1), 44–61 (1973)
Newman, C.M.: Zeros of the partition function for generalized Ising systems. Commun. Pure Appl. Math. 27, 143–159 (1974)
Newman, C.M.: Inequalities for Ising models and field theories which obey the Lee-Yang theorem. Commun. Math. Phys. 41, 1–9 (1975)
Newman, C.M.: Fourier transforms with only real zeros. Proc. Am. Math. Soc. 61, 245–251 (1976)
Newman, C.M.: Normal fluctuations and the FKG inequalities. Commun. Math. Phys. 74(2), 119–128 (1980)
Newman, C.M.: A general central limit theorem for FKG systems. Commun. Math. Phys. 91(1), 75–80 (1983)
Newman, C.M.: Some critical exponent inequalities for percolation. J. Stat. Phys. 45(3), 359–368 (1986)
Newman, C.M.: Another critical exponent inequality for percolation: \(\beta \ge 2/\delta \). J. Stat. Phys. 47(5), 695–699 (1987)
Newman, C.M.: Inequalities for \(\gamma \) and related critical exponents in short and long range percolation. In: Percolation Theory and Ergodic Theory of Infinite Particle Systems, pp. 229–244. Springer, New York (1987)
Newman, C.M.: Disordered Ising systems and random cluster representations. In: Grimmett, G. (ed.) Probability and Phase Transition, pp. 247–260. Kluwer, Dordrecht (1994)
Newman, C.M.: Topics in Disordered Systems. Birkhauser, Basel (1997)
Newman, C.M., Cohen, J.E.: A stochastic theory of community food webs: I. Models and aggregated data. Proc. Royal. Soc. London B224, 421–448 (1985)
Newman, C.M., Cohen, J.E., Kipnis, C.: Neo-Darwinian evolution implies punctuated equilibria. Nature 315, 400–401 (1985)
Newman, C.M., Grimmett, G.R.: Percolation in \(\infty +1\) Dimensions, pp. 167–190. Claredon Press, Oxford (1990)
Newman, C.M., Piza, M.S.T.: Divergence of shape fluctuations in two dimensions. Ann. Probab. 23(3), 977–1005 (1995)
Newman, C.M., Schulman, L.S.: Infinite clusters in percolation models. J. Stat. Phys. 26(3), 613–628 (1981)
Newman, C.M., Schulman, L.S.: One dimensional \(1/|j - i|^s\) percolation models: the existence of a transition for \(s \le 2\). Commun. Math. Phys. 104(4), 547–571 (1986)
Newman, C.M., Stein, D.L.: Unpublished
Newman, C.M., Stein, D.L.: Multiple states and thermodynamic limits in short-ranged Ising spin glass models. Phys. Rev. B 46, 973–982 (1992)
Newman, C.M., Stein, D.L.: Spin-glass model with dimension-dependent ground state multiplicity. Phys. Rev. Lett. 72, 2286–2289 (1994)
Newman, C.M., Stein, D.L.: Ground state structure in a highly disordered spin glass model. J. Stat. Phys. 82, 1113–1132 (1996)
Newman, C.M., Stein, D.L.: Spatial inhomogeneity and thermodynamic chaos. Phys. Rev. Lett. 76, 4821–4824 (1996)
Newman, C.M., Stein, D.L.: Metastate approach to thermodynamic chaos. Phys. Rev. E 55, 5194–5211 (1997)
Newman, C.M., Stein, D.L.: Simplicity of state and overlap structure in finite-volume realistic spin glasses. Phys. Rev. E 57, 1356–1366 (1998)
Newman, C.M., Stein, D.L.: Thermodynamic chaos and the structure of short-range spin glasses. In: Bovier, A., Picco, P. (eds.) Mathematics of Spin Glasses and Neural Networks, pp. 243–287. Birkhauser, Boston (1998)
Newman, C.M., Stein, D.L.: Blocking and persistence in the zero-temperature dynamics of homogeneous and disordered Ising models. Phys. Rev. Lett. 82, 3944–3947 (1999)
Newman, C.M., Stein, D.L.: Equilibrium pure states and nonequilibrium chaos. J. Stat. Phys. 94, 709–722 (1999)
Newman, C.M., Stein, D.L.: Nature of ground state incongruence in two-dimensional spin glasses. Phys. Rev. Lett. 84, 3966–3969 (2000)
Newman, C.M., Stein, D.L.: Are there incongruent ground states in \(2{D}\) Edwards-Anderson spin glasses? Commun. Math. Phys. 224, 205–218 (2001)
Newman, C.M., Stein, D.L.: Interfaces and the question of regional congruence in spin glasses. Phys. Rev. Lett. 87, 077201 (2001)
Newman, C.M., Stein, D.L.: Nonrealistic behavior of mean field spin glasses. Phys. Rev. Lett. 91, 197205 (2003)
Newman, C.M., Stein, D.L.: Topical review: ordering and broken symmetry in short-ranged spin glasses. J. Phys. Condens. Matter 15, R1319–R1364 (2003)
Newman, C.M., Stein, D.L.: Short-range spin glasses: results and speculations. In: Bolthausen, E., Bovier, A. (eds.) Spin Glass Theory, pp. 159–175. Springer, Berlin (2006)
Newman, C.M., Wu, W.: Gaussian fluctuations for the classical XY model. Ann. Inst. H. Poincare (B) 54, 1759–1777 (2018)
Newman, C.M., Wu, W.: Lee-Yang property and Gaussian multiplicative chaos. Commun. Math. Phys. 369, 153–170 (2019)
Newman, C.M., Wu, W.: Constants of deBruijn–Newman type in analytic number theory and statistical physics. Bull. Am. Math. Soc., in press. Published online April 19, 2019. https://doi.org/10.1090/bull/1668
Nguyen, B.G.: Gap exponents for percolation processes with triangle condition. J. Stat. Phys. 49(1), 235–243 (1987)
Nguyen, B.G., Yang, W.S.: Triangle condition for oriented percolation in high dimensions. Ann. Probab. 21(4), 1809–1844 (1993)
Onsager, L.: Crystal statisics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. 65, 117–149 (1944)
Osterwalder, K., Schrader, R.: Axioms for Euclidean Green’s functions. Commun. Math. Phys. 31, 83–112 (1973)
Palassini, M., Caracciolo, S.: Universal finite-size scaling functions in the \(3d\) Ising spin glass. Phys. Rev. Lett. 82, 5128–5131 (1999)
Palassini, M., Young, A.P.: Evidence for a trivial ground-state structure in the two-dimensional Ising spin glass. Phys. Rev. B 60, R9919–R9922 (1999)
Palassini, M., Young, A.P.: Triviality of the ground state structure in Ising spin glasses. Phys. Rev. Lett. 83, 5126–5129 (1999)
Palassini, M., Young, A.P.: Nature of the spin glass state. Phys. Rev. Lett. 85, 3017–3020 (2000)
Parisi, G.: Infinite number of order parameters for spin-glasses. Phys. Rev. Lett. 43, 1754–1756 (1979)
Parisi, G.: Order parameter for spin-glasses. Phys. Rev. Lett. 50, 1946–1948 (1983)
Peierls, R.: On Ising’s model of ferromagnetism. Proc. Cambridge Phil. Soc. 32, 477–481 (1936)
Penrose, O., Lebowitz, J.L.: On the exponential decay of correlation functions. Commun. Math. Phys. 39, 165–184 (1974)
Polyakov, A.M.: Conformal symmetry of critical fluctuations. JETP Lett. 12, 381–383 (1970). [Pisma Zh. Eksp. Teor. Fiz. 12538(1970)]
Polymath, D.H.J.: Effective approximation of heat flow evolution of the Riemann \(\zeta \) function, and a new upper bound for the deBruijn–Newman constant (2019). arXiv:1904.12438
R. Basu, S.S., Sly, A.: Coalescence of geodesics in exactly solvable models of last passage percolation (2017). arXiv:1704.05219
Rammal, R., Toulouse, G., Virasoro, M.A.: Ultrametricity for physicists. Rev. Mod. Phys. 58, 765–788 (1986)
Read, N.: Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking. Phys. Rev. E 90, 032142 (2014)
Reger, J.D., Bhatt, R.N., Young, A.P.: Monte Carlo study of the order-parameter distribution in the four-dimensional Ising spin glass. Phys. Rev. Lett. 64, 1859–1862 (1990)
Richardson, D.: Random growth in a tessellation. Math. Proc. Cambridge Philos. Soc. 74(3), 515–528 (1973)
Rodgers, B., Tao, T.: The De Bruijn–Newman constant is non-negative. arXiv:1801.05914
Rohde, S., Schramm, O.: Basic properties of SLE. Ann. Math. 161(2), 883–924 (2005)
Ruelle, D.: A mathematical reformulation of derrida’s REM and GREM. Commun. Math. Phys. 108, 225–239 (1987)
Rushbrooke, G.S.: On the thermodynamics of the critical region for the Ising problem. J. Chem. Phys. 39(3), 842–843 (1963)
Saouter, Y., Gourdon, X., Demichel, P.: An improved lower bound for the de Bruijn-Newman constant. Math. Comput. 80, 2281–2287 (2011)
Schertzer, E., Sun, R., Swart, J.: The Brownian Web, The Brownian Net, and Their Universality, pp. 270–368. Cambridge University Press, Cambridge (2017)
Schramm, O.: Scaling limits of loop-erased random walks and uniform spanning trees. Israel J. Math. 118(1), 221–288 (2000)
Schramm, O.: A percolation formula. Electron. Commun. Probab. 6(12), 115–120 (2001)
Schramm, O., Sheffield, S., Wilson, D.: Conformal radii for conformal loop ensembles. Commun. Math. Phys. 288, 43–53 (2009)
Sheffield, S.: Exploration trees and conformal loop ensembles. Duke Math. J. 147(1), 79–129 (2009)
Sheffield, S., Werner, W.: Conformal loop ensembles: the Markovian characterization and the loop-soup construction. Ann. Math. 176(3), 1827–1917 (2012)
Sherrington, D., Kirkpatrick, S.: Solvable model of a spin glass. Phys. Rev. Lett. 35, 1792–1796 (1975)
Simon, B., Griffiths, R.B.: The \((\phi ^4)_2\) field theory as a classical Ising model. Commun. Math. Phys. 33(2), 145–164 (1973)
Smirnov, S.: Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits. Comptes Rendus de l’Académie des Sciences - Series I - Mathematics 333(3), 239–244 (2001)
Smirnov, S.: Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model. Ann. Math. 172, 1435–1467 (2010)
Smirnov, S., Werner, W.: Critical exponents for two-dimensional percolation. Math. Res. Lett. 8, 729–744 (2001)
Stauffer, D.: Scaling properties of percolation clusters. In: Castellani, C., Di Castro, C., Peliti, L. (eds.) Disordered Systems and Localization, pp. 9–25. Springer, Heidelberg (1981)
Stauffer, D., Aharony, A.: Introduction to Percolation Theory. Taylor & Francis, London (1994). Revised Second Edition
Stein, D.L.: Frustration and fluctuations in systems with quenched disorder. In: Chandra, P., Coleman, P., Kotliar, G., Ong, P., Stein, D., Yu, C. (eds.) PWA90: A Lifetime of Emergence, pp. 169–186. World Scientific, Singapore (2016)
Stein, D.L., Newman, C.M.: Broken ergodicity and the geometry of rugged landscapes. Phys. Rev. E 51, 5228–5238 (1995)
Stein, D.L., Newman, C.M.: Spin Glasses and Complexity. Princeton University Press, Princeton (2013)
Sun, R., Swart, J.M.: The Brownian net. Ann. Probab. 36(3), 1153–1208 (2008)
Suzuki, M., Fisher, M.E.: Zeros of the partition function for the Heisenberg, ferroelectric, and general Ising models. J. Math. Phys. 12, 235–246 (1971)
Swendsen, R.H., Wang, J.S.: Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett. 58, 86–88 (1987)
Thouless, D.J.: Long-range order in one-dimensional Ising systems. Phys. Rev. 187, 732–733 (1969)
Tóth, B., Werner, W.: The true self-repelling motion. Probab. Theory Relat. Fields 111(3), 375–452 (1998)
Villain, J.: Theory of one-and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet. J. Phys. 36, 581–590 (1975)
Wang, W., Machta, J., Katzgraber, H.G.: Evidence against a mean field description of short-range spin glasses revealed through thermal boundary conditions. Phys. Rev. B 90, 184412 (2014)
Werner, W., Wu, H.: From CLE\((\kappa )\) to SLE\((\kappa,\rho )\)’s. Electron. J. Probab. 18, 1–20 (2013)
Wilson, K.G.: The renormalization group: critical phenomena and the Kondo problem. Rev. Mod. Phys. 47, 773–840 (1975)
Wilson, K.G.: The renormalization group and critical phenomena. Rev. Mod. Phys. 55, 583–600 (1983)
Wilson, K.G., Kogut, J.: The renormalization group and the \(\epsilon \) expansion. Phys. Rep. 12, 75–199 (1974)
Yang, C.N., Lee, T.D.: Statistical theory of equations of state and phase transitions. I. Theory of condensation. Phys. Rev. 87, 404–409 (1952)
Yao, C.L.: Law of large numbers for critical first-passage percolation on the triangular lattice. Electron. Commun. Probab. 19, 1–14 (2014)
Yao, C.L.: Multi-arm incipient infinite clusters in 2D: scaling limits and winding numbers. Ann. Inst. H. Poincaré Probab. Statist. 54, 1848–1876 (2018)
Yao, C.L.: Asymptotics for 2D critical and near-critical first-passage percolation (2018). arXiv:1806.03737
Yao, C.L.: Limit theorems for critical first-passage percolation on the triangular lattice. Stoch. Proc. Appl. 128, 445–460 (2018)
Yucesoy, B., Katzgraber, H.G., Machta, J.: Evidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model. Phys. Rev. Lett. 109, 177204 (2012)
Zamolodchikov, A.B.: Integrals of motion and S-matrix of the (scaled) \(t=t_c\) Ising model with magnetic field. Int. J. Mod. Phys. 4, 4235–4248 (1989)
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Camia, F., Stein, D.L. (2019). Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman. In: Sidoravicius, V. (eds) Sojourns in Probability Theory and Statistical Physics - I. Springer Proceedings in Mathematics & Statistics, vol 298. Springer, Singapore. https://doi.org/10.1007/978-981-15-0294-1_1
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