Some comments on the connection between disordered long range spin glass models and their mean field version

Journal of Physics A: Mathematical and General

Volumn 36, Issue 43, 2003, Pages 10987-10995

  Guerra, Francesco ^a   Toninelli, Fabio Lucio ^b  

^a UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^b EURANDOM   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242509833     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/43/022     Document Type: Article

References (20)

1. Fisher D S and Huse D A 1986 Ordered phase of short-range Ising spin-glasses Phys. Rev. Lett. 56 1601
2. Marinari E, Parisi G, Ricci-Tersenghi F, Ruiz-Lorenzo J and Zuliani F 2000 Replica symmetry breaking in short range spin glasses: a review of the theoretical foundations and of the numerical evidence J. Stat. Phys. 98 973
3. Newman C M and Stein D L 2003 Ordering and broken symmetry in short-ranged spin glasses Preprint cond-mat/0301403
4. Sherrington D and Kirkpatrick S 1975 Solvable model of a spin-glass Phys. Rev. Lett. 35 1792-6
5. Mézard M, Parisi G and Virasoro M A 1987 Spin Glass Theory and Beyond (Singapore: World Scientific)
6. Edwards S F and Anderson P W 1975 Theory of spin glasses J. Phys. F: Met. Phys. 5 1865
7. Lebowitz J L and Penrose O 1966 Rigorous treatment of the van der Waals-Maxwell theory of the liquid-vapor transition J. Math. Phys. 7 98-113
8. Kac M, Uhlenbeck G and Hemmer P C 1963 On the van der Waals theory of vapour-liquid equilibrium. I. Discussion of a one-dimensional model J. Math. Phys. 4 216-28
9. Fröhlich J and Zegarlinski B 1987 Some comments on the Sherrington-Kirkpatrick model of spin glasses Commun. Math. Phys. 112 553-66
10. Bovier A 1998 The Kac version of the Sherrington-Kirkpatrick model at high temperatures J. Stat. Phys. 91 459-74
11. Bovier A, Gayrard V and Picco P 1995 Large deviation principles for the Hopfleld and the Kac-Hopfleld model Probab. Theory Rel. Fields 101 511-46
12. Viana L and Bray A J 1985 Phase diagram for dilute spin-glasses J. Phys. C: Solid State 18 3037-51
13. Guerra F 2003 Broken replica symmetry bounds in the mean field spin glass model Commun. Math. Phys. 233 1-12
14. Franz S and Leone M 2003 Replica bounds for optimization problems and diluted spin systems J. Stat. Phys. 111 535-64
15. Guerra F and Toninelli F L 2002 The thermodynamic limit in mean field spin glass models Commun. Math. Phys. 230 71-9
16. Vuillermot P A 1977 Thermodynamics of quenched random spin systems, and application to the problem of phase transitions in magnetic (spin) glasses J. Phys. A: Math. Gen. 10 1319
17. van Enter A C D and van Hemmen J L 1983 The thermodynamic limit for long-range random systems J. Stat. Phys. 32 141
18. Ruelle D 1969 Statistical Mechanics. Rigorous Results (New York: Benjamin)
19. Guerra F and Toninelli F L 2003 The high temperature region of the Viana-Bray diluted spin glass model J. Stat. Phys. (Preprint cond-mat/0302401)
20. Guerra F 1996 About the overlap distribution in mean field spin glass models Int. J. Mod. Phys. B 10 1674-84