The cavity method for quantum disordered systems: From transverse random field ferromagnets to directed polymers in random media

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2011, Issue 1, 2011, Pages

  Dimitrova, O ^a   Mezard M ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

Disordered systems (theory); Phase diagrams (theory); Quantum phase transitions (theory)

Indexed keywords

EID: 79751520922     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2011/01/P01020     Document Type: Article

References (49)

1. Ioffe L B and Mézard M, 2010 Phys. Rev. Lett. 105 037001
2. Feigel'man M V, Ioffe L B and Mézard M, 2010 Phys. Rev. B 82 184534
3. Mézard M, Parisi G and Virasoro M A, 1985 Europhys. Lett. 1 77
4. Sherrington D and Kirkpatrick S, 1975 Phys. Rev. Lett. 35 1792
5. Parisi G, 1980 J. Phys. A: Math. Gen. 13 1101
6. Parisi G, 1980 J. Phys. A: Math. Gen. 13 L115
7. Parisi G, 1983 Phys. Rev. Lett. 50 1946
8. Mézard M, Parisi G, Sourlas N, Toulouse G and Virasoro M A, 1984 J. Physique 45 843
9. Mézard M, Parisi G and Virasoro M A, 1985 J. Phys. Lett. 46 L217
10. Talagrand M, 2003 C. R. Acad. Sci. Paris I 337 111
11. Guerra F, 2003 Commun. Math. Phys. 233 1
12. Edwards S F and Anderson P W, 1975 J. Phys. F: Met. Phys. 5 965
13. de Almeida J R L and Thouless D, 1978 J. Phys. A: Math. Gen. 11 983
14. Thouless D J, Anderson P W and Palmer R G, 1977 Phil. Mag. 35 593
15. Bray A J and Moore M, 1979 J. Phys. C: Solid State Phys. 13 L469
16. Thouless D J, 1986 Phys. Rev. Lett. 6 1082
17. Chayes J T, Chayes L, Sethna J P and Thouless D J, 1986 Commun. Math. Phys. 106 41
18. Mézard M and Montanari A, 2006 J. Stat. Phys. 124 1317
19. Viana L and Bray A J, 1985 J. Phys. C: Solid State Phys. 18 3037
20. Mézard M and Parisi G, 1987 Europhys. Lett. 3 1067
21. Kanter I and Sompolinsky H, 1987 Phys. Rev. Lett. 58 164
22. Mézard M and Parisi G, 2001 Eur. Phys. J. B 20 217
23. For a recent review, see Mézard M and Montanari A, 2009 Information, Physics, and Computation' (Oxford: Oxford University Press)
24. Abou-Chacra R, Anderson P W and Thouless D J, 1973 J. Phys. C: Solid State Phys. 6 1734
25. Sachdev S, 2000 Quantum Phase Transitions (Cambridge: Cambridge University Press)
26. MacCoy B M and Wu T T, 1968 Phys. Rev. 176 631
27. Fisher D S, 1992 Phys. Rev. Lett. 69 534
28. Fisher D S, 1994 Phys. Rev. B 50 3799
29. Ma S, Dasgupta C and Hu C, 1979 Phys. Rev. Lett. 43 1434
30. Dasgupta C and Ma S, 1980 Phys. Rev. B 22 1305
31. Young A P and Rieger H, 1996 Phys. Rev. B 53 8486
32. Iglói F and Rieger H, 1998 Phys. Rev. 57 11404
33. For a review, see Iglói F and Monthus C, 2005 Phys. Rep. 412 277
34. Pich C et al, 1998 Phys. Rev. Lett. 81 5916
35. Rieger H and Kawashima N, 1999 Eur. Phys. J. B 9 233
36. Motrunich O, Mau S-C, Huse D A and Fisher D S, 2000 Phys. Rev. B 61 1160
37. Yu R, Saleur H and Haas S, 2008 Phys. Rev. B 77 140402
38. Kovács I A and Iglói F, 2010 Phys. Rev. B 82 054437
39. Kovács I A and Iglói F, 2010 arXiv:1010.2344v1
40. Ma M, Halperin B and Lee P, 1986 Phys. Rev. B 34 3136
41. Laumann C, Scardicchio A and Sondhi S L, 2008 Phys. Rev. B 78 134424
42. Krzakala F, Rosso A, Semerjian G and Zamponi F, 2008 Phys. Rev. B 78 134428
43. Blöte H W J and Deng Y, 2002 Phys. Rev. E 66 066110
44. Derrida B and Spohn H, 1988 J. Stat. Phys. 51 817
45. Cook J and Derrida B, 1990 J. Phys. A: Math. Gen. 23 1523
46. Mézard M, Parisi G and Virasoro M, 1987 Spin Glass Theory and Beyond (Singapore: World Scientific)
47. Derrida B, 1981 Phys. Rev. B 24 2613
48. Gross D J and Mézard M, 1984 Nucl. Phys. B 240 431
49. Zamponi F, 2010 private communication