Magnetic and glassy transitions in the square-lattice XY model with random phase shifts

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2010, Issue 3, 2010, Pages

  Alba, Vincenzo ^a   Pelissetto, Andrea ^b   Vicari, Ettore ^c  

^a INFN SEZIONE DI PISA   (Italy)

^b UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^c UNIVERSITY OF PISA   (Italy)

Author keywords

Classical Monte Carlo simulations; Classical phase transitions (theory); Critical exponents and amplitudes (theory); Spin glasses (theory)

Indexed keywords

EID: 77950243293     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2010/03/P03006     Document Type: Article

References (90)

1. Granato E and Kosterlitz J M 1986 Quenched disorder in Josephson-junction arrays in a transverse magnetic field Phys. Rev. B 33 6533
2. Granato E and Kosterlitz J M 1989 Disorder in Josephson-junction arrays in a magnetic field Phys. Rev. Lett. 62 823
3. Rubinstein M, Shrainam B and Nelson D R 1983 Two-dimensional XY magnets with random Dzyaloshinskii-Moriya interactions Phys. Rev. B 27 1800
4. Cha M-C and Fertig H A 1994 Orientational order and depinning of the disordered electron solid Phys. Rev. Lett. 73 870 [arXiv:cond-mat/9402021]
5. Cha M-C and Fertig H A 1994 Topological defects, orientational order, and depinning of the electron solid in a random potential Phys. Rev. B 50 14368 [arXiv:cond-mat/9409001]
6. Fisher M P A, Tokuyasu T A and Young A P 1991 Vortex variable-range- hopping resistivity in superconducting films Phys. Rev. Lett. 66 2931
7. Korshunov S E 2006 Phase transitions in two-dimensional systems with continuous degeneracy Usp. Fiz. Nauk 176 233
8. Korshunov S E 2006 Phys. Usp. 49 225 (Engl. Transl.)
9. Kawashima N and Rieger H 2004 Recent progress in spin glasses Frustrated Spin Systems ed H T Diep (Singapore: World Scientific) [arXiv:cond-mat/0312432]
10. Ozeki Y and Nishimori H 1993 Phase diagram of gauge glasses J. Phys. A: Math. Gen. 26 3399
11. Nishimori H 2002 Exact results on spin glass models Physica A 306 68 [arXiv:cond-mat/0201056]
12. Ebner C and Stroud D 1985 Diamagnetic susceptibility of superconducting clusters: spin-glass behavior Phys. Rev. B 31 165
13. Forrester M G, Lee H J, Tinkhams M and Lobb C J 1988 Positional disorder in Josephson-junction arrays: experiments and simulations Phys. Rev. B 37 5966
14. Chakrabarti A and Dasgupta C 1988 Phase transition in positionally disordered Josephson-junction arrays in a transverse magnetic field Phys. Rev. B 37 7557
15. Forrester M G, Benz S P and Lobb C J 1990 Monte Carlo simulations of Josephson-junction arrays with positional disorder Phys. Rev. B 41 8749
16. Huse D A and Seung H S 1990 Possible vortex-glass transition in a model random superconductor Phys. Rev. B 42 1059
17. Reger J D, Tokuyasu T A, Young A P and Fisher M P A 1991 Vortex-glass transition in three dimensions Phys. Rev. B 44 7147
18. Li Y-H 1992 Voltage-current characteristics of the two-dimensional gauge glass model Phys. Rev. Lett. 69 1819
19. Gingras M J P 1992 Numerical study of vortex-glass order in random-superconductor and related spin-glass models Phys. Rev. B 45 7547
20. 7 - δ films Phys. Rev. Lett. 69 2717
21. Reger J D and Young A P 1993 Monte Carlo study of a vortex glass model J. Phys. A: Math. Gen. 26 L1067 [arXiv:cond-mat/9311036]
22. Korshunov S E 1993 Possible destruction of the ordered phase in Josephson-junction arrays with positional disorder Phys. Rev. B 48 1124
23. Nishimori H and Kawamura H 1993 Gauge glass ordering in two dimensions J. Phys. Soc. Japan. 62 3266
24. Nishimori H 1994 Gauge glass, spin glass and coding theory: Exact results Physica A 205 1
25. Nattermann T, Scheidl S, Korshunov S E and Li M S 1995 Absence of reentrance in the two-dimensional XY model with random phase shifts J. Physique I 5 565 [arXiv:cond-mat/9501120]
26. Cha M-C and Fertig H A 1995 Disorder-induced phase transitions in two-dimensional crystals Phys. Rev. Lett. 74 4867
27. Jeon G S, Kim S and Choi M Y 1995 Phase transition in the XY gauge glass Phys. Rev. B 51 16211
28. Hyman R A, Wallin M, Fisher M P A, Girvin S M and Young A P 1995 Current-voltage characteristics of two-dimensional vortex-glass models Phys. Rev. B 51 15304 [arXiv:cond-mat/9409117]
29. Korshunov S E and Nattermann T 1996 Absence of reentrance in superconducting arrays with positional disorder Phys. Rev. B 53 2746
30. Tang L-H 1996 Vortex statistics in a disordered two-dimensional XY model Phys. Rev. B 54 3350 [arXiv:cond-mat/9602162]
31. Bokil H S and Young A P 1996 Study of chirality in the two-dimensional XY spin glass J. Phys. A: Math. Gen. 29 L89 [arXiv:cond-mat/9512042]
32. Maucourt J and Grempel D R 1997 Phase transitions in the two-dimensional XY model with random phases: a Monte Carlo study Phys. Rev. B 56 2572 [arXiv:cond-mat/9703109]
33. Scheidl S 1997 Glassy vortex state in a two-dimensional disordered XY model Phys. Rev. B 55 457 [arXiv:cond-mat/9601131]
34. Kosterlitz J M and Simkin M V 1997 Numerical study of a superconducting glass model Phys. Rev. Lett. 79 1098 [arXiv:cond-mat/9702166]
35. Kim B J, Choi M Y, Ryu S and Stroud D 1997 Anomalous relaxation in the XY gauge glass Phys. Rev. B 56 6007 [arXiv:cond-mat/9707140]
36. Maucourt J and Grempel D R 1998 Scaling of domain-wall energies in the three-dimensional gauge glass model Phys. Rev. B 58 2654
37. Carpentier D and Le Doussal P 1998 Disordered XY models and Coulomb gases: renormalization via traveling waves Phys. Rev. Lett. 81 2558 [arXiv:cond-mat/9802083]
38. Granato E 1998 Current-voltage scaling of chiral and gauge-glass models of two-dimensional superconductors Phys. Rev. B 58 11161 [arXiv:cond-mat/ 9808331]
39. 7 - δ thin films Phys. Rev. B 58 2868
40. Kosterlitz J M and Akino N 1999 Numerical study of spin and chiral order in a two-dimensional XY spin glass Phys. Rev. Lett. 82 4094 [arXiv:cond-mat/ 9806339]
41. Mudry C and Wen X-G 1999 Does quasi-long-range order in the two-dimensional XY model really survive weak random phase fluctuations? Nucl. Phys. B 549 613 [arXiv:cond-mat/9712146]
42. Choi M Y and Park S Y 1999 Phase transition in the two-dimensional gauge glass Phys. Rev. B 60 4070 [arXiv:cond-mat/9906326]
43. Kim B J 2000 Finite-temperature resistive transition in the two-dimensional XY gauge glass model Phys. Rev. B 62 644 [arXiv:cond-mat/ 0004069]
44. Carpentier D and Le Doussal P 2000 Topological transitions and freezing in XY models and Coulomb gases with quenched disorder: renormalization via traveling waves Nucl. Phys. B 588 565 [arXiv:cond-mat/9908335]
45. Akino N and Kosterlitz J M 2002 Domain wall renormalization group study of the XY model with quenched random phase shifts Phys. Rev. B 66 054536 [arXiv:cond-mat/0203299]
46. Holme P and Olsson P 2002 A zero-temperature study of vortex mobility in two-dimensional vortex glass models Europhys. Lett. 60 439 [arXiv:cond-mat/ 0111555]
47. Katzgraber H G and Young A P 2002 Numerical studies of the two-and three-dimensional gauge glass at low temperature Phys. Rev. B 66 224507 [arXiv:cond-mat/0205206]
48. Katzgraber H G 2003 On the existence of a finite-temperature transition in the two-dimensional gauge glass Phys. Rev. B 67 180402(R) [arXiv:cond-mat/0305393]
49. Katzgraber H G 2003 Numerical studies of the two-and three-dimensional gauge glass at low temperature J. Appl. Phys. 93 7661 [arXiv:cond-mat/0304540]
50. Holme P, Kim B J and Minnhagen P 2003 Phase transitions in the two-dimensional random gauge XY model Phys. Rev. B 67 104510 [arXiv:cond-mat/0301279]
51. Chen Q-H, Tanaka A and Hu X 2003 Evidence for finite-temperature glass transition in two dimensions Physica B 329 1413
52. Nikolaou M and Wallin M 2004 Zero-temperature glass transition in the two-dimensional gauge glass model Phys. Rev. B 69 184512 [arXiv:cond-mat/ 0312066]
53. Katzgraber H G and Campbell I A 2005 Dynamical scaling in Ising and vector spin glasses Phys. Rev. B 72 014462 [arXiv:cond-mat/0504082]
54. Tang L-H and Tong P 2005 Zero-temperature criticality in the two-dimensional gauge glass model Phys. Rev. Lett. 94 207204 [arXiv:cond-mat/0412415]
55. Um J, Kim B J, Minnaghen P, Choi M Y and Lee S-I 2006 Dynamic critical behaviors in two-dimensional Josephson junction arrays with positional disorder Phys. Rev. B 74 094516 [arXiv:cond-mat/0608390]
56. Yun Y J, Baek I C and Choi M Y 2006 Experimental study of positionally disordered Josephson junction arrays Europhys. Lett. 76 271 [arXiv:cond-mat/ 0509151]
57. Chen Q-H, Lv J-P and Liu H 2008 Dynamics of glass phases in the two-dimensional gauge glass model Phys. Rev. B 78 054519 arXiv:0812.2822
58. Alba V, Pelissetto A and Vicari E 2009 Quasi-long-range order in the 2D XY model with random phase shifts J. Phys. A: Math. Theor. 42 295001 [arXiv:0901.4682]
59. Ristivojevic Z 2009 Superconducting film with randomly magnetized dots: a realization of the two-dimensional XY model with random phase shifts Phys. Rev. B 80 174528 [arXiv:0903.5514]
60. Kosterlitz J M and Thouless D J 1973 Ordering, metastability and phase transitions in two-dimensional systems J. Phys. C: Solid State Phys. 6 1181
61. Hasenbusch M and Pinn K 1997 Computing the roughening transition of Ising and solid-on-solid models by BCSOS model matching J. Phys. A: Math. Gen. 30 63 [arXiv:cond-mat/9605019]
62. Hasenbusch M, Marcu M and Pinn K 1994 High-precision renormalization- group study of the roughening transition Physica A 208 124 [arXiv:hep-lat/ 9404016]
63. Nishimori H 1981 Internal energy, specific heat and correlation function of the bond-random Ising model Prog. Theor. Phys. 66 1169
64. Hasenbusch M, Parisen Toldin F, Pelissetto A and Vicari E 2008 Multicritical Nishimori point in the phase diagram of the J Ising model on a square lattice Phys. Rev. E 77 051115 [arXiv:0803.0444]
65. Picco M, Honecker A and Pujol P 2006 Strong disorder fixed points in the two-dimensional random-bond Ising model J. Stat. Mech. P09006 [arXiv:cond-mat/0606312]
66. Hasenbusch M, Parisen Toldin F, Pelissetto A and Vicari E 2008 Universal dependence on disorder of two-dimensional randomly diluted and random-bond J Ising models Phys. Rev. E 78 011110 [arXiv:0804.2788]
67. Parisen Toldin F, Pelissetto A and Vicari E 2009 Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice J Ising model J. Stat. Phys. 135 1039 [arXiv:0811.2101]
68. Parisen Toldin F, Pelissetto A and Vicari E 2010 in preparation
69. Amoruso C and Hartmann A K 2004 Domain-wall energies and magnetization of the two-dimensional random-bond Ising model Phys. Rev. B 70 134425 [arXiv:cond-mat/0401464]
70. Wang C, Harrington J and Preskill J 2003 Confinement-Higgs transition in a disordered Gauge theory and the accuracy threshold for quantum memory Ann. Phys., NY 303 31 [arXiv:quant-ph/0207088]
71. Campostrini M, Pelissetto A, Rossi P and Vicari E 1996 Strong-coupling analysis of two-dimensional O(N) models with N ≤ 2 on square, triangular, and honeycomb lattices Phys. Rev. B 54 7301 [arXiv:hep-lat/9603002]
72. Balog J, Niedermaier M, Niedermayer F, Patrascioiu A, Seiler E and Weisz P 2001 Does the XY model have an integrable continuum limit? Nucl. Phys. B 618 315 [arXiv:hep-lat/0106015]
73. 3) Nucl. Phys. B 575 579 [arXiv:cond-mat/9911452]
74. Pelissetto A and Vicari E 1998 Four-point renormalized coupling constant and Callan-Symanzik β-function in O(N) models Nucl. Phys. B 519 123 [arXiv:cond-mat/9711078]
75. Pelissetto A and Vicari E 2002 Critical phenomena and renormalization-group theory Phys. Rep. 368 549 [arXiv:cond-mat/0012164]
76. Geyer C J 1991 Markov chain Monte Carlo maximum likelihood Computer Science and Statistics: Proc. of the 23rd Symp. on the Interface ed E M Keramidas (Fairfax Station, VA: Interface Foundation) p156
77. Hukushima K and Nemoto K 1996 Exchange Monte Carlo method and application to spin glass simulations J. Phys. Soc. Japan 65 1604
78. Earl D J and Deem M W 2005 Parallel tempering: theory, applications, and new perspectives Phys. Chem. Chem. Phys. 7 3910 [arXiv:physics/0508111]
79. Hasenbusch M, Pelissetto A and Vicari E 2008 Critical behavior of three-dimensional Ising spin glass models Phys. Rev. B 78 214205 [arXiv:0809.3329]
80. Hasenbusch M, Pelissetto A and Vicari E 2008 The critical behavior of 3D Ising spin glass models: universality and scaling corrections J. Stat. Mech. L02001 [arXiv:0710.1980]
81. Hasenbusch M, Parisen Toldin F, Pelissetto A and Vicari E 2007 The universality class of 3D site-diluted and bond-diluted Ising systems J. Stat. Mech. P02016 [arXiv:cond-mat/0611707]
82. Amit D J, Goldschmidt Y Y and Grinstein G 1980 Renormalisation group analysis of the phase transition in the 2D Coulomb gas, sine-Gordon theory and XY-model J. Phys. A: Math. Gen. 13 585
83. Balog J and Hegedũs A 2000 Two-loop beta-functions of the sine-Gordon model J. Phys. A: Math. Gen. 33 6543 [arXiv:hep-th/0003258]
84. Balog J 2001 Kosterlitz-Thouless theory and lattice artifacts J. Phys. A: Math. Gen. 34 5237 [arXiv:hep-lat/0011078]
85. Kosterlitz J M 1974 The critical properties of the two-dimensional xy model J. Phys. C: Solid State Phys. 7 1046
86. José J V, Kadanoff L P, Kirkpatrick S and Nelson D R 1978 Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model Phys. Rev. B 16 1217
87. Wegner F J 1976 The Critical State (General Aspects in Phase Transitions and Critical Phenomena vol 6) ed C Domb and M Green (New York: Academic) p7
88. Campostrini M, Pelissetto A, Rossi P and Vicari E 2002 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice Phys. Rev. E 65 066127 [arXiv:cond-mat/0201180]
89. Hasenbusch M, Parisen Toldin F, Pelissetto A and Vicari E 2007 Magnetic-glassy multicritical behavior of the three-dimensional J Ising model Phys. Rev. B 76 184202 arXiv:0707.2866
90. Binder K and Young A P 1986 Spin glasses: experimental facts, theoretical concepts, and open questions Rev. Mod. Phys. 58 801