Abstract
In the past few years, new approaches to Monte Carlo simulations have produced substantial improvements in efficiency for both simulation and data analysis. This paper reviews recent developments in simulational methods to overcome problems due to the long relaxation times related to “critical slowing down”, under the general category of “cluster methods”. We also discuss general “histogram methods” for improving the efficiency of the data analysis. These methods are described along with their advantages, disadvantages and some new applications.
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References
N. Metropolis, A.W. Rosenbluth. M.N. Rosenbluth, A.H. Teller, E. Teller: J. Chem. Phys. 21, 1087 (1953)
K.G. Wilson: Phys. Rev. D 10, 2445 (1974); and in Recent Developments in Gauge Theories, ed. by G. ‘t Hooft et al. ( Plenum, New York 1980 )
K. Binder: Phys. Rev. Lett. 47, 693 (1981)
K. Binder: J. Comput. Phys. 59, 1 (1985)
K. Binder (ed.): Monte Carlo Methods in Statistical Physics, Topics Curr. Phys. Vol. 7, 2nd edn. (Springer, Berlin, Heidelberg 1986); K. Binder (ed.): Applications of the Monte Carlo Method in Statistical Physics, Topics Curr. Phys., Vol. 36, 2nd edn. ( Springer, Berlin, Heidelberg 1987 )
J.A. McCammon, S.C. Harvey: Dynamics of Proteins and Nucleic Acids (Cambridge University Press, New York 1987), and references therein
C.H. Brooks III, M. Karplus, B.M. Pettitt: Proteins: A theoretical perspective of dynamics, structure and thermodynamics, in Advances in Chemical Physics, Vol. LXXI, ed. by I. Prigogine, S. Rice (Wiley, New York 1988 )
P.C. Hohenberg, B.I. Halperin: Rev. Mod. Phys. 49, 435 (1977)
G. Parisi: In Progress in Gauge Field Theory, ed. by G. ‘t Hooft et al. ( Plenum, New York 1984 ) p. 531;
G.G. Batrouni G.R. Katz, A.S. Kronfeld, G.P. Lepage, B. Svetitsky, K.G. Wilson: Phys. Rev. D 32, 2736 (1985);
E. Dagotto, J. Kogut: Phys. Rev. Lett. 58, 299 (1987)
J. Goodman, A.D. Sokal: Phys. Rev. Lett. 56, 1015 (1986);
J. Goodman, A.D. Sokal: Phys. Rev. D 40, 2035 (1989)
D. Kandel, E. Domany, D. Ron, A. Brandt, E. Loh: Phys. Rev. Lett. 60, 1591 (1988)
D. Kandel, E. Domany, A. Brandt: Phys. Rev. B 40, 330 (1988)
R. Ben-Av, D. Kandel, E. Katznelson, P.G. Lauwers, S. Solomon: J. Stat. Phys. 58, 125 (1990)
D. Kandel, R. Ben-Av, E. Domany: Phys. Rev. Lett. 65, 941 (1990)
K.E. Schmidt: Phys. Rev. Lett. 51, 2175 (1983);
M. Faas, H.J. Hilhorst: Physica A 135, 571 (1986);
H.H. Hahn, T.S.J. Streit: Physica A 154, 108 (1988);
E.P. Stoll: J. Phys. Condens. Matter 1, 6959 (1989)
M. Creutz: Phys. Rev. D 36, 515 (1987);
F.R. Brown, T.J. Woch: Phys. Rev. Lett. 58, 2394 (1987);
S.L. Adler: Phys. Rev. D 38, 1349 (1988)
R.H. Swendsen, J.-S. Wang: Phys. Rev. Lett. 58, 86 (1987)
P.W. Kasteleyn, C.M. Fortuin: J. Phys. Soc. J.n. Suppl. 26s, 11 (1969);
C.M. Fortuin, P.W. Kasteleyn: Physica (Utrecht) 57, 536 (1972)
D. Stauffer: Phys. Rep. 54, 1 (1979);
J.W. Essam: Rep. Prog. Phys. 43, 830 (1980)
U. Wolff: Phys. Rev. Lett. 60, 1461 (1988);
U. Wolff: Nucl. Phys. B 300 [FS22], 501 (1988)
F. Niedermayer: Phys. Rev. Lett. 61, 2026 (1988)
R.G. Edwards, A.D. Sokal: Phys. Rev. D 38, 2009 (1988)
U. Wolff: Phys. Rev. Lett. 62, 361 (1989)
U. Wolff: Phys. Lett. B 228, 379 (1989)
U. Wolff: Nucl. Phys. B 322, 759 (1989)
R.G. Edwards, A.D. Sokal: Phys. Rev. D 40, 1374 (1989)
W. Janke: Phys. Lett. A 148, 306 (1990)
R.C. Brower, P. Tamayo: Phys. Rev. Lett. 62, 1087 (1989)
J.-S. Wang, R.H. Swendsen, R. Koteckÿ: Phys. Rev. Lett. 63, 109 (1989)
J.-S. Wang, R.H. Swendsen, R. Koteckÿ: Phys. Rev. B 42, 2465 (1990)
M. Hasenbusch: Nucl. Phys. B 333, 581 (1990)
Ch. Frick, K. Jansen, P. Seuferling: Phys. Rev. Lett. 63, 2613 (1989)
M. Hasenbusch, S. Meyer: Phys. Rev. Lett. 66, 530 (1991)
W. Klein, T. Ray, P. Tamayo: Phys. Rev. Lett. 62, 163 (1989)
T.S. Ray, P. Tamayo, W. Klein: Phys. Rev. A 39, 5949 (1989)
D.W. Heermann, A.N. Burkitt: Physica A 162, 210 (1990)
X.-J. Li, A.D. Sokal: Phys. Rev. Lett. 63, 827 (1989);
X.-J. Li, A.D. Sokal: Phys. Rev. Lett. 67, 1482 (1991)
J.-S. Wang: Physica A 164, 240 (1990)
P. Tamayo, R.C. Brower, W. Klein: J. Stat. Phys. 58, 1083 (1990)
A.M. Ferrenberg, R.H. Swendsen: Phys. Rev. Lett. 61, 2635 (1988)
D.A. Chesnut, Z.W. Salsburg: J. Chem. Phys. 38, 2861 (1963)
A.M. Ferrenberg, R.H. Swendsen: Phys. Rev. Lett. 63, 1195 (1989)
A.M. Ferrenberg, R.H. Swendsen: Comput. in Phys. 101 (Sept./Oct. 1989 )
R.H. Swendsen, A.M. Ferrenberg: In Computer Simulation Studies in Condensed Matter Physics II. ed. by D.P. Landau, K.K. Mon, H.-B. Schüttler, Springer Proc. Phys., Vol. 45 ( Springer, Berlin, Heidelberg 1990 )
C.H. Bennett: J. Comput. Phys. 22, 245 (1976)
S. Huang, K.J.M. Moriarty, E. Myers, J. Potvin: Preprint (1990)
S. Huang, E. Myers, K.J.M. Moriarty, J. Potvin: Preprint (1990)
Z.W. Salsburg, J.D. Jackson, W. Fickett, W.W. Wood: J. Chem. Phys. 30, 65 (1959)
I.R. McDonald, K. Singer: Discuss. Faraday Soc. 43, 40 (1967)
J.P. Valleau, D.N. Card: J. Chem. Phys. 57, 5457 (1972)
G. Torrie, J.P. Valleau: Chem. Phys. Lett. 28, 578 (1974);
G. Torrie, J.P. Valleau: J. Comput. Phys. 23, 187 (1977)
M. Falcioni, E. Marinari, M.L. Paciello, G. Parisi, B. Taglienti: Phys. Lett. 108B, 331 (1982)
E. Marinari: Nucl. Phys. B 235 [FS11], 123 (1984)
C.N. Yang, T.D. Lee: Phys. Rev. 87, 404 (1952)
G. Bhanot, S. Black, P. Carter, R. Salvador: Phys. Lett. B 183, 331 (1987)
G. Bhanot, K.M. Bitar, S. Black, P. Carter, R. Salvador: Phys. Lett. B 187, 381 (1987)
G. Bhanot, K.M. Bitar, R. Salvador: Phys. Lett. B 188, 246 (1987)
G. Bhanot, R. Salvador, S. Black, R. Tòral: Phys. Rev. Lett. 59, 803 (1987)
N.A. Alves, B.A. Berg, R. Villanova: Phys. Rev. B 41, 383 (1990)
G.V. Bhanot, S. Sanielev: Phys. Rev. D 40, 3454 (1989)
M. Fukugita, M. Okawa, A. Ukawa: Phys. Rev. Lett. 63, 1768 (1989)
W. Bock, H.G. Evertz, J. Jersâk, D.P. Landau, T. Neuhaus, J.L. Xu: Phys. Rev. D 41, 2573 (1990)
S. Gottlieb, W. Liu, R.L. Renken, R.L. Sugar, D. Toussaint: Phys. Rev. D 40, 2389 (1989)
R.V. Gavai, F. Karsch: Phys. Lett B 233, 417 (1989)
M. Fukugita, H. Mine, M. Okawa, A. Ukawa: KEK preprint 89–74
W. Janke, H. Kleinert: Phys. Lett. A 140, 513 (1989)
N. Caticha, J. Chahine, H.R. Drugowich de Félicio: Phys. Rev. A 40, 7431 (1989)
J. Chahine, H.R. Drugowich de Félicio, N. Caticha: Phys. Lett. A 139, 360 (1989)
E.P. Munger, M.A. Novotny: J. Phys. A, to be published
F. Mallezie: Phys. Rev. B 41, 4475 (1990)
A.M. Ferrenberg, D.P. Landau: Preprint
H. Müller-Krumbhaar, K. Binder: J. Stat. Phys. 8, 1 (1973)
A. Coniglio, W. Klein: J. Phys. A 13, 2775 (1980)
C.-K. Hu: Phys. Rev. B 29, 5103, 5109 (1984)
J. Hoshen, R. Kopelman: Phys. Rev. B 14, 3438 (1976)
C.F. Baillie, P.D. Coddington: Concurrency: Practice and Experience 3, 129 (1991)
H. Mino: Preprint
A.N. Burkitt, D.W. Heermann: Parallel Comput. 13, 345 (1990)
C.-K. Hu, K.-S. Mak: Phys. Rev. B 40, 5007 (1989)
M.D. De Meo, D.W. Heermann, K. Binder: J. Stat. Phys. 60, 585 (1990)
F. Niedermayer: Phys. Lett. B 237, 473 (1990)
M. Sweeny: Phys. Rev. B 27, 4445 (1983)
M. Hasenbusch, S. Meyer: Phys. Lett. B 241, 238 (1990)
J.-S. Wang, W. Selke, VI.S. Dotsenko, V.B. Andreichenko, Europhys. Lett. 11, 301 (1990);
J.-S. Wang, W. Selke, VI.S. Dotsenko, V.B. Andreichenko, Physica A 164, 221 (1990)
J.-S. Wang and D. Chowdhury: J. de Phys. 50, 2905 (1989);
J.-S. Wang, M. Wöhlert, H. Mühlenbein, D. Chowdhury: Physica A 166, 173 (1990)
Z. Alexandrowicz: Physica A 160, 310 (1989)
J.-S. Wang: Physica A 161, 249 (1989)
A. Coniglio, F. Liberto, G. Monroy, F. Peruggi: J. Phys. A: Math. Gen. 22, L837 (1989)
J.-S. Wang, D. Stauffer: Z. Phys. B 78, 145 (1990)
A.N. Burkitt, D.W. Heermann: Europhys. Lett. 10, 207 (1989)
D. Stauffer: Physica A 162, 27 (1989)
T.S. Ray, P. Tamayo: J. Stat. Phys. 60, 851 (1990)
T.S. Ray, J.-S. Wang: Physica A 167, 580 (1990)
J.-S. Wang, R.H. Swendsen: Physica A 167, 565 (1990)
L.-J. Chen, C.-K. Hu, K.-S. Mak: Comput. Phys. Commun. (1991), Preprint
R.H. Swendsen, J.-S. Wang: Phys. Rev. Lett. 57, 2607 (1986)
J.-S. Wang, R.H. Swendsen: Phys. Rev. B 38, 4840 (1988)
J.-S. Wang, R.H. Swendsen: Phys. Rev. B 38, 9086 (1988)
J.-S. Wang, R.H. Swendsen: Phys. Rev. B 37, 7745 (1988)
R.N. Bhatt, A.P. Young: Phys. Rev. Lett. 54, 924 (1985)
A.T. Ogielski, I. Morgenstern: Phys. Rev. Lett. 54, 928 (1985)
A.T. Ogielski: Phys. Rev. B 32, 7384 (1985)
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Swendsen, R.H., Wang, JS., Ferrenberg, A.M. (1992). New Monte Carlo Methods for Improved Efficiency of Computer Simulations in Statistical Mechanics. In: Binder, K. (eds) The Monte Carlo Method in Condensed Matter Physics. Topics in Applied Physics, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02855-1_4
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