Equilibrium statistical mechanics of frustrated spin glasses : a survey of mathematical results

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1. [1] M. Aizenman, J.L. Lebowitz and D. Ruelle, Some rigorous results on the Sherrington-Kirkpatrick model, Commun. Math. Phys., Vol. 112, 1987, pp. 3-20. Zbl1108.82312MR904135
2. [2] M. Aizenman and J. Wehr, Rounding of first order phase transitions in systems with quenched disorder, Commun. Math. Phys., Vol. 130, 1990, pp. 489-528. Zbl0714.60090MR1060388
3. [3] J.R.L. Almeida and D.J. Thouless, Stability of the Sherrington-Kirkpatrick solution of a spin glass model, J. Phys. A. Math. Gen., Vol. 11, 1978, pp. 983-990. 
4. [4] J.M.G. Amaro De Matos, A.E. Patrick and V.A. Zagrebnov, Random infinite volume Gibbs states for the Curie-Weiss random field Ising model, J. Stat. Phys., Vol. 66, 1992, pp. 139-164. Zbl0925.60127MR1149483
5. [5] D.J. Amit, H. Gutfreund and H. Sompolinsky, Spin-glass models of neural networks, Phys. Rev., A32, 1985, pp. 1007-1018. MR797031
6. [6] L.A. Bassalygo and R.L. Dobrushin, Uniqueness of a Gibbs field with random potential: an elementary approach, Th. Prob. Appl., Vol. 31, 1988, pp. 572-589. Zbl0635.60107
7. [7] G. Ben Arous and A. Guionnet, Huge symmetric Langevin spin glass dynamics, preprint Université de Paris XI, 1994. Zbl0954.60031MR1457623
8. [8] C.E. Bezuidenhout, G.R. Grimmett and H. Kesten, Strict inequalities for critical values of Potts models and random chluster processes, preprint Bristol Université;, 1992. Zbl0783.60100
9. [9] K. Binder and A.P. Young, Spin glasses: experimental facts, theoretical concepts, and open questions, Rev. Mod. Phys., Vol. 58, 1988, pp. 801-976. 
10. [10] K. Binder, Y. Imry and E. Pytte, Interface roughening and random field instabilities, Phys. Rev., B24, 1981, pp. 6736-6739. 
11. [11] P.M. Bleher, The Bethe lattice spin glass at zero temperature, Ann. Inst. H. Poincaré, Vol. 54, 1991, pp. 89-113. Zbl0719.60123MR1102973
12. [12] A. Bovier, Disordered systems and random geometry: polymers, spin glasses, interfaces, Ph. D. dissertation, ETH Zurich, 1986. 
13. [13] A. Bovier and J. Fröhlich, A heuristic theory of the spin glass phase, J. Stat. Phys., Vol. 44, 1986, pp. 347-391. MR857062
14. [14] A. Bovier, V. Gayrard and P. Picco, Gibbs states of the Hopfield model with extensively many patterns, preprint Weiersrass IAAS, Berlin, 1994. Zbl1081.82570MR1325589
15. [15] A. Bovier, V. Gayrard and P. Picco, Large deviation principales for the Hopfield and Kac-Hopfield models, preprint CPT Marseille, 1994. Zbl0826.60090MR1305586
16. [16] J. Bricmont and A. Kupiainen, Phase transition in the three-dimensional random field Ising model, Commun. Math. Phys., Vol. 116, 1988, pp. 539-572. Zbl1086.82573MR943702
17. [17] J. Bricmont and A. Kupiainen, Random walk in asymmetric random environments, Commun. Math. Phys., Vol. 142, 1991, pp. 345-420. Zbl0734.60112MR1137068
18. [18] E. Buffet, A. Patrick and J.V. Pulé, Directed polymers on trees: a martingale approach, J. Phys. A: Math. Gen., Vol. 26, 1993, pp. 1823-1834. Zbl0773.60035MR1220795
19. [19] M. Campanino and E. Olivieri, One dimensional random Ising system with interaction decay r-(1+∈); a convergent cluster expansion, Commun. Math. Phys., Vol. 111, 1987, pp. 555-557. Zbl0642.60103MR901154
20. [20] M. Campanino, E. Olivieri and A. C.D. Van Enter, One dimensional spin glass with interaction decay r-(1+∈); a convergent cluster expansion, Commun. Math. Phys., Vol. 108, 1987, pp. 241-255. Zbl0615.60099MR875301
21. [21] M. Cassandro, E. Olivieri and B. Tirozzi, Infinite differentiability for one dimensional spin systems with long range interactions, Commun. Math. Phys., Vol. 87, 1982, pp. 229-252. Zbl0506.58009MR684101
22. [22] D. Caprocaccia, M. Cassandro and P. Picco, On the existence of thermodynamics for the generalised random energy model, J. Stat. Phys., Vol. 46, 1987, pp. 493-505. MR883541
23. [23] S. Caracciolo, G. Parisi and N. Sourlas, Low temperature behaviour of three dimensional spin glasses in a magnetic field, J. Phys. France, Vol. 51, 1990, pp. 1877-1895. 
24. [24] J.T. Chalker, On the lower critical dimensionality of the Ising model in a random field, J. Phys. C: Sol. State Phys., Vol. 16, 1983, pp. 6615-6622. 
25. [25] B. Chauvin and A. Rouault, Boltmann-Gibbs wights in the branching random walk, IMA workshop on branching processes, June 1994, to appear in the proceedings. Zbl0866.60074MR1601693
26. [26] D. Chowdhury, Spin glasses and other frustrated systems, World Scientific, Singapore, 1986. 
27. [27] J. Chayes, L. Chayes and J. Fröhlich, The low temperature behaviour of disordered magnets, Commun. Math. Phys., Vol. 100, 1985, pp. 399-437. MR802552
28. [28] J. Chayes, L. Chayes, J.P. Sethna and D.J. Thouless, A mean field spin glass with short-range interactions, Commun. Math. Phys., Vol. 106, 1986, pp. 41-89. MR853978
29. [29] P. Collet and J.P. Eckmann, Spin glass model with random couplings, Commun. Math. Phys., Vol. 93, 1984, pp. 379-406. Zbl0553.60098MR745692
30. [30] P. Collet and F. Koukiou, Large deviations for the multiplicative chaos, Commun. Math. Phys., Vol. 147, 1992, pp. 329-342. Zbl0755.60022MR1174416
31. [31] F. Comets and J. Neveu, The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: the high temperature case, preprint CMAP École Polytechnique, 1993. Zbl0811.60098MR1312435
32. [32] F. Comets, A spherical bound for the Sherrington-Kirkpatrick model, preprint Unviersité de Paris VII, 1994. MR1417976
33. [33] P. Contucci, On the strict inequality between quenched and annealed Ising spin glass, preprints SISSA, 1993, to appear in Lett. Math. Phys. Zbl0768.60096MR1213613
34. [34] B. Derrida, Random energy model: limit of a family of disordered models, Phys. Rev. Lett., Vol. 45, 1980, pp. 79-82. MR575260
35. [35] B. Derrida and H. Spohn, Polymers on disordered trees, spin glasses, and travelling waves, J. Stat. Phys., Vol. 51, 1988, pp. 817-840. Zbl1036.82522MR971033
36. [36] B. Derrida, M.R. Evans and E.R. Speer, Mean-field theory of directed polymers with random complex weights, preprint SPhT, 1992, to appear in Commun. Math. Phys. Zbl0779.60077MR1233845
37. [37] R. Dobrushin, The description of a random field by means of conditional probabilities and conditions of its regularity, Theor. Prob. Appl., Vol. 13, 1968, pp. 197-224. Zbl0184.40403MR231434
38. [38] C. De Dominicis and M. Hilhorst, Random free energies in spin glasses, J. Phys. Lett., Vol. 46, 1985, pp. L909-L914. 
39. [39] H. von Dreifus, A. Klein and J. Fernando Perez, Taming Griffiths' singularities: infinite differentiability of quenched correlation functions, preprint UCLA, 1994 to appear in Commun. Math. Phys. Zbl0820.60086MR1331689
40. [40] S.F. Edwards and P.W. Anderson, Theory of spin glasses, J. Phys. F: Metal Phys., Vol. 5, 1975, pp. 965-974. 
41. [41] A.C.D. Van Enter, One-dimensional spin glasses; uniqueness and cluster properties, J. Phys. A: Math. Gen., Vol. 21, 1988, pp. 1781-1786. MR952725
42. [42] A.C.D. Van Enter, Stiffness exponents, number of pure states, and Almeida-Thouless lines in spin glasses, J. Stat. Phys., Vol. 60, 1990, pp. 275-279. Zbl1086.82575MR1063219
43. [43] A.C.D. Van Enter and J.L. Van Hemmen, Statistical mechanical formalism for sign glasses, Phys. Rev. A, Vol. 29, 1984, pp. 355-365. MR729632
44. [44] A.C.D. Van Enter and J.L. Van Hemmen, Thermodynamic limit for long-range spin glasses, J. Stat. Phys., Vol. 32, 1985, pp. 141-152. 
45. [45] A.C.D. Van Enter and J. Fröhlich, Absence of symmetry breaking for N-vector spin glass models in two dimensions, Commun. Math. Phys., Vol. 98, 1985, pp. 425-432. Zbl1223.82059MR788782
46. [46] A.C.D. Van Enter and R. Griffiths, The order parameter in a spin glass, Commun. Math. Phys., Vol. 90, 1983, pp. 319-327. MR719293
47. [47] A.C.D. van Enter and J. Miękisz, Breaking of periodicity at positive temperatures, Commun. Math. Phys., Vol. 134, 1990, pp. 647-651. Zbl0711.60109MR1086748
48. [48] D. Espriu, M. Gross, P.E.L. Rakow and J.F. Wheater, Continuum limit on a two-dimensional random lattice, Nucl. Phys., Vol. B265 [FS 15], 1986, pp. 92-112. 
49. [49] D.S. Fisher, J. Fröhlich and T. Spencer, The Ising model in a random magnetic field, J. Stat. Phys., Vol. 34, 1984, pp. 863-870. MR751717
50. [50] D.S. Fisher and D.A. Huse, Pure phases in spin glasses, J. Phys. A: Math. Gen., Vol. 20, 1987, pp. L997-L1003; Absence of many states in magnetic spin glasses, J. Phys. A: Math. Gen., Vol. 20, 1987, pp. L1005-L1010. 
51. [51] J. Fröhlich, Mathematical aspects of the physics of disordered systems, in Critical phenomena, random systems, and gauge theories, K OSTERWALDER, R. STORA Eds. pp. 725-894, North-Holland, Amsterdam, 1986. Zbl0669.60098MR880538
52. [52] J. Fröhlich and J. Imbrie, Improved perturbation expansion for disordered systems: beating Griffiths singularities, Commun. Math. Phys., Vol. 96, 1984, pp. 145-180. Zbl0574.60098MR768253
53. [53] J. Fröhlich and B. Zegarlinski, The disordered phase of long-range Ising spin glasses, Europhys. Lett., Vol. 2, 1986, pp. 53-60. 
54. [54] J. Fröhlich and B. Zegarlinski, The high temperature phase of long range spin glasses, Commun. Math. Phys., Vol. 110, 1987, pp. 121-155. MR885574
55. [55] J. Fröhlich and B. Zegarlinski, Some comments on the Sherrington-Kirkpatrick model of spin glasses, Commun. Math. Phys., Vol. 112, 1987, pp. 553-566. MR910578
56. [56] J. Fröhlich and B. Zegarlinski, Spin glasses and other lattice systems with long range interactions, Commun. Math. Phys., Vol. 120, 1989, pp. 665-688. Zbl0661.60128MR987774
57. [57] A. Galves, S. Martínez and P. Picco, Fluctuations in Derrida's random energy and generalised random energy models, J. Stat. Phys., Vol. 54, 1989, pp. 515-529. MR984264
58. [58] E. Gardner, A spin glass on a hierarchical lattice, J. Phys. France, Vol. 45, 1984, pp. 1755-1763. MR769601
59. [59] C.P.M. Geerse and A. Hof, Lattice gas models on self-similar aperiodic tilings, Rev. Math. Phys., Vol. 3, 1991, pp. 163-221. Zbl0743.60115MR1121468
60. [60] A. Georges, M. Mézard and J. Yedidia, Low temperature phase of the Ising spin glass on a hypercubic lattice, Phys. Rev. Lett., Vol. 64, 1990, pp. 2937-2940. Zbl1050.82558MR1055998
61. [61] A. Georges, D. Hansel, P. Le Doussal, J.M. Maillard and J. Bouchaud, Rigorous bounds for 2D disordered Ising models, J. Phys. France, Vol. 47, 1986, pp. 947-953. 
62. [62] H.O. Georgii, Spontaneous magnetisation of randomly dilute ferromagnets, J. Stat. Phys., Vol. 25, 1981, pp. 369-396. MR630351
63. [63] V.L. Girko, Theory of random determinants, Kluwer Academic Publ., Dodrecht, 1990. MR1080966
64. [64] E. Goles and S. Martínez, The one-site distribution of Gibbs states on the Bethe lattice are probability vectors of period ≤ 2 for a nonlinear transformation, J. Stat. Phys., Vol. 52, 1988, pp. 267-285. Zbl1082.82506MR968586
65. [65] S. Goulart-Rosa, The thermodynamic limit of quenched free energy of magnetic systems with random interactions, J. Phys. A: Math. Gen., Vol. 15, 1982, pp. L51-L54. MR638300
66. [66] R.B. Griffiths, Nonalytic behaviour above the critical point in a random Ising ferromagnet, Phys. Rev. Lett., Vol. 23, 1969, pp. 17-19. 
67. [67] G.R. Grimmett, The stochastic random cluster process and the uniqueness of random cluster measures, preprint Cambridge, 1994. 
68. [68] F. Guerra, Fluctuations and thermodynamic variables in mean field spin glass models, preprint Roma-La Sapienza, 1992. Zbl0835.60099
69. [69] F. Guerra, The cavity method in the mean field spin glass model. Functional representations of thermodynamic variables, preprint Roma - La Sapienza, 1994. MR1414694
70. [70] F. Guerra, Functional order parameters for the quenched free energy in mean field spin glass model, preprint Roma - La Sapienza, 1992. MR1428232
71. [71] J.L. Van Hemmen, Classical spin glasses model, Phys. Rev. Lett., Vol. 49, 1982, pp. 409-412. MR668161
72. [72] J.L. Van Hemmen and I. Morgenstern Eds., Heidelberg colloquium on spin glasses, Lect. Notes Phys., Vol. 192, 1983. MR733796
73. [73] J.J. Hopfield, Neural networks and physical systems with emergent collective computational capabilities, Proc. Natl. Acad. Sci. USA, Vol. 79, 1982, pp. 2554-2588. MR652033
74. [74] J. Imbrie, The ground states of the three-dimensional random field Ising model, Commun. Math. Phys., Vol. 98, 1985, pp. 145-176 Zbl1223.82016MR786570
75. [75] Y. Imry, Random external fields, J. Stat. Phys., Vol. 34, 1984, pp. 849-862. 
76. [76] J.P. Kahane, Multiplications aléatoires et dimension de Hausdorff, Ann. Inst. H. Poincaré, Vol. 23, 1987, pp. 289-296. Zbl0619.60005MR898497
77. [77] K.M. Khanin, Absence of phase transition in one-dimensional long-range spin systems with random interactions, Theor. Math. Phys., Vol. 43, 1980, pp. 445-449. 
78. [78] K.M. Khanin and Ya Sinai, Existence of free energy for models with long-range random Hamiltonian, J. Stat. Phys., Vol. 20, 1979, pp. 573-584. MR537262
79. [79] S. Kirkpatrick and D. Sherrington, Infinite-ranged models of spin glasses, Phys. Rev. B, Vol. 17, 1978, pp. 4384-4403. 
80. [80] H. Koch, A free energy bound for the Hopfield model, J. Phys. A: Math. Gen., Vol. 26, 1993, pp. L353-L355. Zbl0775.82008MR1212003
81. [81] R. Kotecký and E. Olivieri, Droplet dynamics for asymmetric Ising model, J. Stat. Phys., Vol. 70, 1993, pp. 1121-1148. Zbl1081.82591MR1208633
82. [82] A.M. Khorunzy, B.A. Khoruzhenko, L.A. Pastur and M. Shcherbina, Large n limit in statistical mechanics and spectral theory of disordered systems, in Phase transitions and critical phenomena (DOMB and LEBOWITZ Eds.), Vol. 15, 1992, pp. 74-241, Academic Press, London. 
83. [83] F. Koukiou, Rigorous bounds for the free energy of short range Ising spin glass model, Europhys. Lett., Vol. 17, 1992, pp. 669-671. MR1158147
84. [84] F. Koukiou, A random covering interpretation for the phase transition of the random energy model, J. Stat. Phys., Vol. 60, 1990, pp. 669-674. Zbl1086.82544MR1076915
85. [85] F. Koukiou, private communication, 1994. 
86. [86] F. Koukiou, D. Petritis and M. Zahradník, Extension of the Pirogov-Sinai theory to a class of quasiperiodic interactions, Commun. Math. Phys., Vol. 118, 1988, pp. 365-383. Zbl0668.58013MR958802
87. [87] F. Koukiou and P. Picco, Poisson point processes, cascades, and random coverings of Rn, J. Stat. Phys., Vol. 62, 1991, pp. 481-489. Zbl0741.60111MR1105270
88. [88] W. Krauth and O. Pluchery, A rapid dynamical Monte Carlo algorithm for glassy systems, J. Phys. A: Math. Gen., Vol. 27, 1994, pp. L715-L720. Zbl0850.82045MR1306164
89. [89] O.E. Lanford and D. Ruelle, Observable at infinity and states with short range correlations in statistical mechanics, Commun. Math. Phys., Vol. 13, 1969, pp. 194-215. MR256687
90. [90] B. Lautrup, Uniqueness of Parisi's scheme for replica symmetry breaking, Ann. Phys.NY, Vol. 216, 1992, pp. 73-97. Zbl0875.20004MR1163416
91. [91] M. Ledoux and M. Talagrand, Probability in Banach spaces, Springer-Verlag, Berlin, 1991. Zbl0748.60004MR1102015
92. [92] F. Ledrappier, Pressure and variational principle for random Ising model, Commun. Math. Phys., Vol. 56, 1977, pp. 297-302. Zbl0367.60116MR456186
93. [93] L. Lovász, Combinatorial problems and exercises, North-Holland, Amsterdam, 1993. Zbl0785.05001MR1265492
94. [94] T.C. Lubensky, Critical properties of random spin models from ∈ expansions, Phys. Rev. B, Vol. 11, 1975, pp. 3573-3580. 
95. [95] R.J. Mceliece, The theory of information and coding, Encyclopedia of Mathematics, Addison-Wesley, Reading, 1977. Zbl0376.94011MR469516
96. [96] E. Marinari, G. Parisi and F. Ritort, Replica field theory for determinisitic models: binary sequences with low autocorrelation, preprint Roma-La Sapienza, 1994, available from hep-th@babbage.sissa.it under the reference 9405148. Zbl0843.60096
97. [97] E. Marinari, G. Parisi and F. Ritort, Replica field theory for determinisitic models: non random spin glasses with glassy behaviour, preprint Roma-La Sapienza, 1994, available from cond-mat@babbage.sissa.it under the reference 9406074. Zbl0843.60097
98. [98] E. Marinari, G. Parisi, F. Ritort, On the 3d Ising spin, preprint Roma-La Sapienza, 1993, available from cond-mat@babbage.sissa.it under the reference 9310041. 
99. [99] F. Martinelli, Dynamical analysis of the low temperature cluster algorithms, J. Stat. phys., Vol. 66, 1992, pp. 1245-1276. Zbl0925.82181MR1156404
100. [100] F. Martinelli, E. Olivieri and E. Scoppola, On the Swendsen-Wang dynamics I: Exponential convergence to the equilibrium, J. Stat. Phys., Vol. 62, 1991, pp. 117-133. Zbl0739.60097MR1105259
101. [101] F. Martinelli, E. Olivieri and E. Scoppola, On the Swendsen-Wang dynamics II: Critical droplets and homogeneous nucleation at low temperature, J. Stat. Phys., Vol. 62, 1991, pp. 135-159. Zbl0739.60098MR1105260
102. [102] S. Martínez and D. Petritis, Brownian bridge polymer model in a random environment, J. Phys. A: Math. Gen., 1996, in press. Zbl0919.60078MR1385633
103. [103] J. Mémin, private communication, 1994. 
104. [104] M. Mézard, G. Parisi and M. Virasoro, Spin glass theory and beyond, World Scientific, Singapore, 1987. Zbl0992.82500MR1026102
105. [105] M. Mézard, G. Parisi and M. Virasoro, The replica solution without replicas, Europhys. Lett., Vol. 1, 1986, pp. 77-82. 
106. [106] M. Mézard, G. Parisi, N. Sourlas, G. Toulouse and M. Virasoro, Nature of the spin-glass phase, Phys. Rev. Lett., Vol. 52, 1984, pp. 1156-1159. Zbl0968.82528
107. [107] J. Miękisz, A microscopic model with quasicrystalline properties, J. Stat. Phys., Vol. 58, 1990, pp. 1137-1146. MR1049061
108. [108] C.M. Newman, Memory capacity in neural network model: rigorous lower bounds, Neural Net., Vol. 1, 1988, pp. 223-238. 
109. [109] C.M. Newman and D.L. Stein, Multiple states and thermodynamic limites in short ranged Ising spin glass models, Phys. Rev. B, Vol. 46, 1992, pp. 973. 
110. [110] C.M. Newman and D.L. Stein, Non-mean-field behaviour of realistic spin glasses, preprint New York University, 1995, available from adap-org@xyz.lanl.gov under reference 9508006. 
111. [111] A. Ogielski and I. Morgenstern, Critical behaviour of the three dimensional Ising spin glass model, Phys. Rev. Lett., Vol. 54, 1985, pp. 928-931. 
112. [112] E. Olivieri and P. Picco, On the existence of thermodynamics for the random energy model, Commun. Math. Phys., Vol. 96, 1984, pp. 125-144. Zbl0585.60098MR765963
113. [113] G. Parisi, Infinite number of order parameters for spin glasses, Phys. Rev. Lett., Vol. 43, 1979, pp. 1754-1756. 
114. [114] G. Parisi, A sequence of approximated solutions to the Sherrington-Kirkpatrick model for spin glasses, J. Phys. A: Math. Gen., Vol. 13, 1980, pp. L115-L121. 
115. [115] G. Parisi, The order parameter for spin glasses: a function on the interval [0, 1], J. Phys. A: Math. Gen., Vol. 13, 1980, pp. 1101-1112. 
116. [116] G. Parisi,, Magnetic properties of spin glasses in a new mean field theory, J. Phys. A: Math. Gen., Vol. 13, 1980, pp. 1887-1895. 
117. [117] L. Pastur, Statistical physics and spectral theory of disordered systems: some recent developments, in Proc. X-th International conference of mathematical physics (Leipzig, 1991), Springer-Verlag, Berlin, 1992. Zbl0947.82506MR1386398
118. [118] L. Pastur and A. Figotin, Theory of disordered spin systems, Theor. Math. Phys., Vol. 35, 1978, pp. 403-414. MR503349
119. [119] L. Pastur and A. Figotin, Spectra of random and almost periodic operators, Springer-Verlag, Berlin, 1992. Zbl0752.47002MR1223779
120. [120] L. Pastur and M. Shcherbina, Absence of self-averaging of the order parameter in the Sherrington-Kirkpatrick model, J. Stat. Phys., Vol. 62, 1991, pp. 1-19. MR1105253
121. [121] L. Pastur, M. Shcherbina and B. Tirozzi, The replica symmetric solution without replica trick for the Hopfield model, J. Stat. Phys., Vol. 74, 1994, pp. 1161-1183. Zbl0835.60092MR1268789
122. [122] D. Petritis, The zero-level set of the Brownian bridge as a model of disordered physical systems, in Proc. prob. Theory and Math. Statistics Vol. 2 (Vilnius, 1989), Mosklas, Vilnius, 1990. Zbl0726.60080MR1153883
123. [123] D. Petritis, Thermodynamics for the zero-level set of the Brownian bridge, Commun. Math. Phys., Vol. 125, 1989, pp. 579-595. Zbl0679.60081MR1024928
124. [124] D. Petritis, Thermodynamic formalism of neural computing, Lectures given in the IV-th summer school on Statistical Physics and cooperative systems, Santiago de Chile, 12-16 December 1994, preprint Université de Rennes-I, 1995, available from mp-arc@math.utexas.edu under reference 95-221. MR1421794
125. [125] D. Petritis, Simulations numériques Monte Carlo, preprint Université de Rennes-I, 1993, to be published by Masson, Paris, 1995. 
126. [126] P. Picco, Verres de spin, Thèse d'État, Université de Marseille-II, 1988. 
127. [127] P. Picco, Rigorous results on spin glasses: a review, Rev. Math. Appl., Vol. 12, 1991, pp. 157-169. MR1130608
128. [128] P. Picco, Upper bound on the decay of correlations in the plane rotator model with long-range random interaction, J. Stat. Phys., Vol. 36, 1984, pp. 489-516. Zbl0586.60099MR780678
129. [129] L.E. Pontin, J.A. Baêta Segundo and J. Fernando Perez, Dilute antiferromagnets: Imry-Ma argument, hierarchical model, and equivalence to random field Ising models, J. Stat. Phys., Vol. 75, 1994, pp. 51-65. Zbl0828.60090MR1273053
130. [130] P. Révesz, Random walks in random and non random environments, World Scientific, Singapore, 1990. Zbl0733.60091MR1082348
131. [131] M.A. Ruderman and C. Kittel, Indirect exchange coupling of nuclear magnetic moments by conduction electrons, Phys. Rev., Vol. 96, 1954, pp. 99-102. 
132. [132] D. Ruelle, A mathematical reformulation of Derrida's REM and GREM, Commun. Math. Phys., Vol. 108, 1987, pp. 225-239. Zbl0617.60100MR875300
133. [133] M. Shcherbina and B. Tirozzi, The free energy of a class of Hopfield models, J. Stat. Phys., Vol. 72, 1993, pp. 113-125. Zbl1097.82551MR1233028
134. [134] D. Sherrington, and S. Kirkpatrick, Solvable model of a spin glass, Phys. Rev. Lett., Vol. 35, 1975, pp. 1792-1796. 
135. [135] D. Szász, communication, 1992. 
136. [136] M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, preprint Université Paris-VI, 1994. Zbl0864.60013MR1361756
137. [137] M. Talagrand, A new look at independence, preprint Université de Paris-VI, 1995. MR1387624
138. [138] S.R.S. Varadhan, Private communication, 1992. 
139. [139] P. Vuillermot, Thermodynamics of quenched random spin systems and applications to the proble of phase transitions in magnetic spin glass, J. Phys. A: Math. Gen., Vol. 10, 1977, pp. 1319-1333. MR452421
140. [140] F. Vermet, Asymptotic study of a neural network: the Hopfield deterministic sequential dynamics, preprint Université de Rennes-I, 1994. 
141. [141] F. Vermet, Étude asymptotique d'un réseau neuronal, Thèse de doctorat, Université de Rennes-I, 1994. 
142. [142] E.C. Waymire and S.C. Williams, Correlated spin glasses on trees, IMA workshop on branching processes, June 1994, to appear in the proceedings. 
143. [143] P. Whittle, Random fields on random graphs, Adv. Appl. Prob., Vol. 24, 1992, pp. 455-473. Zbl0753.60102MR1167267
144. [144] H. Wilf, Generatingfunctionology, Academic Press, Boston, 1994. Zbl0831.05001MR1277813
145. [145] B. Zegarlinski, Interactions and pressure functionals for disordered lattice systems, Commun. Math. Phys., Vol. 139, 1991, pp. 305-339. Zbl0747.58066MR1120141
146. [146] B. Zegarlinski, Spin glass with long range interactions at high temperature, J. Stat. Phys., Vol. 17, 1987, pp. 911-930. MR912509