Abstract
I review several problems dealing with the equilibrium behavior of classical two dimensional Josephson junction arrays in applied magnetic fields. Specific attention is given to the cases of a uniform field with average flux density per unit cell of f=0, f=1/2, f=1/q and f=1/2−1/q. Several models incorporating the effects of randomness on the Josephson array are also reviewed. These include the case of a random vortex pinning potential and its effects on vortex lattice order, and the spin glass, gauge glass, and positionally disordered array.
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Bagchi K., Anderson H. C., Swope W. (1996): Computer simulation study of the melting transition in two dimensions. Phys. Rev. Lett. 76, 255
Benz S. P., Forrester M. G., Tinkham M., Lobb C. J. (1988): Positional disorder in superconducting wire networks and Josephson junction arrays. Phys. Rev. B 38, 2869
Bokil H. S., Young A. P. (1996): Study of chirality in the two-dimensional XY spin glass. Preprint, cond-mat/9512042
Caillol J. M., Levesque D., Weis J. J., Hansen J. P. (1982): A Monte Carlo study of the classical two-dimensional one-component plasma. J. Stat. Phys. 28, 325
Caillol J. M., Levesque D. (1986): Low-density phase diagram of the two-dimensional Coulomb gas. Phys. Rev. B 33, 499
Chakrabarti A., Dasgupta C. (1988): Phase transition in positionally disordered Josephson-junction arrays in a transverse magnetic field. Phys. Rev. B 37, 7557
Choi M. Y., Chung J. S., Stroud D. (1987): Positional disorder in a Josephsonjunction array. Phys. Rev. B 35 1669
Choquard Ph., Clerouin J. (1983): Cooperative phenomena below melting of the one-component two-dimensional plasma. Phys. Rev. Lett. 50, 2086
Chudnovsky E. M. (1991): Orientational and positional order in flux lattices of type-II superconductors. Phys. Rev. B 43, 7831
Cieplak M., Banavar J. R., Li M. S., Khurana A. (1992): Frustration, scaling, and local gauge invariance. Phys. Rev. B 45, 786
Cohn M. B., Rzchoswki M. S., Benz S. P., Lobb C. J. (1991): Vortex-defect interactions in Josephson-junction arrays. Phys. Rev. B 43, 12823
Dodgson M. J. W. (1995): Investigation on the ground states of a model thin film superconductor on a sphere. Preprint, cond-mat/9512124
Fisher D. S. (1980): Flux-lattice melting in a thin-film superconductor. Phys. Rev. B 22, 1190
Fisher M. P. A., Tokuyasu T. A., Young A. P. (1991): Vortex variable-rangehopping resistivity in superconducting films. Phys. Rev. Lett. 66, 2931
Forrester M. B., Lee H. J., Tinkham M., Lobb C. J. (1988): Positional disorder in Josephson-junction arrays: Experiments and simulations. Phys. Rev. B 37, 5966
Forrester M. G., Benz S. P., Lobb C. J. (1990): Monte Carlo simulations of Josephson-junction arrays with positional disorder. Phys. Rev. B 41, 8749
Fradkin E., Huberman B. A., Shenker S. H. (1978): Gauge symmetries in random magnetic systems. Phys. Rev. B 18, 4789
Franz M., Teitel S. (1995): Vortex-lattice melting in two-dimensional superconducting networks and films. Phys. Rev. B 51 6551
Franz M., Teitel S. (1996): Effect of random pinning on 2D vortex lattice correlations. In preparation
Friesen M. (1995): Critical and non-critical behavior of the Kosterlitz-Thouless-Berezinskii transition. Phys. Rev. B 53, R514
Giamarchi T., Le Doussal P. (1994): Elastic theory of pinned flux lattices. Phys. Rev. Lett. 72, 1530
Gingras M. J. P. (1992): Numerical study of vortex-glass order in randomsuperconductor and related spin-glass models. Phys. Rev. B 45, 7547
Giovannella C., Tinkham M., eds. (1995): Macroscopic Quantum Phenomena and Coherence in Superconducting Networks. (World Scientific, Singapore)
Granato E., Kosterlitz J. M. (1986): Quenched disorder in Josephson-junction arrays in a transverse magnetic field. Phys. Rev. B 33, 6533
Granato E., Nightingale M. P. (1993): Chiral exponents of the square-lattice frustrated XY model: a Monte Carlo transfer-matrix calculation. Phys. Rev. B 48, 7438
Grest G. S. (1989): Critical behavior of the two-dimensional uniformly frustrated charged Coulomb gas. Phys. Rev. B 39, 9267
Gupta P., Teitel S. (1996): Phase diagram of the 2D dense lattice Coulomb gas. In preparation
Halsey T. C. (1985): Josephson-junction array in an irrational magnetic field: A superconducting glass? Phys. Rev. Lett. 55, 1018
Halsey T. C. (1988): On the critical current of a Josephson junction array in a magnetic field. Physica B 152, 22
Hattel S. A., Wheatley J. M. (1994): Depinning phase transitions in two-dimensional lattice Coulomb solids. Phys. Rev. B 50 16590
Hattel S. A., Wheatley J. M. (1995): Flux lattice melting and depinning in the weakly frustrated two-dimensional XY model. Phys. Rev. B 51, 11951
Hu J., MacDonald A. H. (1993): Two-dimensional vortex lattice melting. Phys. Rev. Lett. 71, 432
José J. V., Kadanoff L. P., Kirkpatrick S., Nelson D. R. (1977): Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model. Phys. Rev. B 16, 1217
Kato Y., Nagaosa N. (1993): Monte Carlo simulation of two-dimensional flux-linelattice melting. Phys. Rev. B 48, 7383
Kawamura H., Tanemura M. (1987): Chiral order in a two-dimensional XY spin glass. Phys. Rev. B 36, 7177
Knops Y. M. M., Nienhuis B., Knops H. J. F., Blöte J. W. J. (1994): 19-vertex version of the fully frustrated XY model. Phys. Rev. B 50, 1061
Kolahchi M. R., Straley, J. P. (1991): Ground state of the uniformly frustrated two-dimensional XY model near f=1/2. Phys. Rev. B 43, 7651
Korshunov S. E. (1986): Phase transitions in two-dimensional uniformly frustrated XY models. II. General scheme. J. Stat. Phys. 43, 17
Korshunov S. E. (1993): Replica symmetry breaking in vortex glasses. Phys. Rev. B 48, 3669
Kosterlitz J. M., Thouless D. (1973): Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181
Kosterlitz J. M. (1974): The critical properties of the two-dimensional xy model. J. Phys. C. 7, 1046
Larkin A. I., Ovchinnikov Yu. N. (1979) Pinning in type II superconductors. J. Low Temp. Phys. 34, 409
Lee D. H., Joannopoulos J. D., Negele J. W., Landau D. P. (1986): Symmetry analysis and Monte Carlo study of a frustrated antiferromagnetic planar (XY) model in two dimensions. Phys. Rev. B 33, 450
Lee J., Kosterlitz J. M., Granato E. (1991): Monte Carlo study of frustrated XY models on a triangular and square lattice. Phys. Rev. B 43, 11531
Lee J.-R. (1994): Phase transitions in the two-dimensional classical lattice Coulomb gas of half-integer charges. Phys. Rev. B 49, 3317
Lee J.-R., Teitel S. (1992): Phase transitions in classical two-dimensional lattice Coulomb gases. Phys. Rev. B 46, 3247
Lee S., Lee K.-C. (1994): Phase transitions in the fully frustrated XY model studied by the microcanonical Monte Carlo technique. Phys. Rev. B 49, 15184
Lee S., Lee K.-C. (1995): Phase transitions in the uniformly frustrated XY model with frustration parameter f=1/3 studied with use of the microcanonical Monte Carlo technique. Phys. Rev. B 52, 6706
Levin Y., Li X., Fisher M. E. (1994): Coulombic criticality in general dimensions. Phys. Rev. Lett. 73, 2716
Li Y.-H., Teitel S. (1990): Flux flow resistance in frustrated Josephson junction arrays. Phys. Rev. Lett. 65, 2595
Li Y.-H., Teitel S. (1991): The effect of random pinning sites on behavior in Josephson junction arrays. Phys. Rev. Lett. 67, 2894
Lidmar J., Wallin M. (1996): Monte Carlo simulation of a two-dimensional continuum Coulomb gas. Preprint, cond-mat/9607025
Lobb C. J., Abraham D. W., Tinkham M. (1983): Theoretical interpretation of resistive transition data from arrays of superconducting weak links. Phys. Rev. B 27, 150 (1983)
Minnhagen P. (1987): The two-dimensional Coulomb gas, vortex unbinding, and superfluid-superconducting films. Rev. Mod. Phys. 59, 1001
Minnhagen P., Wallin M. (1987): New phase diagram for the two-dimensional Coulomb gas. Phys. Rev. B 36, 5620
Minnhagen P., Wallin M. (1989): Results for the phase diagram of the two-dimensional Coulomb gas. Phys. Rev. B 40, 5109
Miyshita S., and Shiba H. (1984): Nature of the phase transition of the two-dimensional antiferromagnetic plane rotor model on the triangular lattice. J. Phys. Soc. Jpn. 53, 1145
Nattermann T., Scheidl S., Korshunov S. E., Li M. S. (1995): Absence of reentrance in the two-dimensional XY-model with random phase shifts. J. Phys. I France 5, 565
Nelson D. R., Halperin B. I. (1979): Dislocation-mediated melting in two dimensions. Phys. Rev. B 19, 2457
Nicolaides D. B. (1991): Monte Carlo simulation of the fully frustrated XY model. J. Phys. A 24, L231
Nightingale M. P., Granato E., Kosterlitz J. M. (1995): Conformal anomaly and critical exponents of the XY Ising model. Phys. Rev. B 52, 7402
Ohta T., Jasnow D. (1979): XY model and the superfluid density in two dimensions. Phys. Rev. B 20, 139
Olsson P. (1995a): Monte Carlo analysis of the two-dimensional XY model. II. Comparison with the Kosterlitz renormalization group equations. Phys. Rev. B 52, 4511
Olsson P. (1995b): Two phase transitions in the fully frustrated XY model. Phys. Rev. Lett. 75, 2758
Ozeki Y., Nishimori H. (1993): Phase diagram of gauge glasses. J. Phys. A 26, 3399
Ramirez-Santiago G., José J. V. (1994): Critical exponents of the fully frustrated two-dimensional XY model. Phys. Rev. B 49, 9567
Ray P., Moore M. A. (1992): Chirality-glass and spin-glass correlations in the two-dimensional random-bond XY model. Phys. Rev. B 45, 5361
Rubinstein M., Shraiman B., Nelson D. R. (1983): Two-dimensional XY magnets with random Dzyaloshinskii-Moriya interactions. Phys. Rev. B 27, 1800
Rzchowski M. S., Benz S. P., Tinkham M., Lobb C. J. (1990): Vortex pinning in Josephson-junction arrays. Phys. Rev. B 42, 2041
Šášik R., Stroud D. (1994): Calculation of the shear modulus of a two-dimensional vortex lattice. Phys. Rev. B 49, 16074
Scheidl S. (1996): Glassy vortex state in a two-dimensional XY-model. Preprint, cond-mat/9601131
Straley J. P. (1988): Magnetic field effects in Josephson networks. Phys. Rev. B 38, 11225
Straley J. P., Barnett G. M. (1993): Phase diagram for a Josephson network in a magnetic field. Phys. Rev. B 48, 3309
Standburg K. J. (1988): Two-dimensional melting. Rev. Mod. Phys. 60, 69
Tang L.-H. (1996): Vortex statistics in a disordered two-dimensional XY model. Preprint, cond-mat/9602162
Teitel S., Jayaprakash C. (1983a): Phase transitions in frustrated two dimensional XY models. Phys. Rev. B 27, 598
Teitel S., Jayaprakash C. (1983b): Josephson junction arrays in transverse magnetic fields. Phys. Rev. Lett. 51, 1999
Tešanović Z., Xing L. (1991): Critical fluctuations in strongly type-II quasi-two-dimensional superconductors. Phys. Rev. Lett. 67, 2729
Théron R., Korshunov S. E., Simond J. B., Leemann Ch., Martinoli P. (1994): Observation of domain-wall superlattice states in a frustrated triangular array of Josephson junctions. Phys. Rev. Lett. 72, 562
Thijssen J. M., Knops H. J. F. (1988a): Monte Carlo study of the Coulomb-gas representation of frustrated XY models. Phys. Rev. B 37, 7738
Thijssen J. M., Knops H. J. F. (1988b): Analysis of a new set of renormalization equations for the Kosterlitz-Thouless transition. Phys. Rev. B 38, 9080
Thijssen J. M., Knops H. J. F. (1990): Monte Carlo transfer-matrix study of the frustrated XY model. Phys. Rev. B 42, 2438
Vallat A., Beck H. (1992): Classical frustrated XY model: Continuity of the groundstate energy as a function of the frustration. Phys. Rev. Lett. 68, 3096
Vallat A., Beck H. (1994): Coulomb-gas representation of the two-dimensional XY model on a torus. Phys. Rev. B 50, 4015
Villain J. (1975): Theory of one-and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet. J. Phys. (Paris) 36, 581
Young A. P. (1979): Melting of the vector Coulomb gas in two dimensions. Phys. Rev. B 19, 1855
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Teitel, S. (1997). Equilibrium phase transitions in Josephson junction arrays. In: Rubí, M., Pérez-Vicente, C. (eds) Complex Behaviour of Glassy Systems. Lecture Notes in Physics, vol 492. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104839
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DOI: https://doi.org/10.1007/BFb0104839
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