Self organization in the low temperature region of a spin glass model

Reviews in Mathematical Physics

Volumn 15, Issue 1, 2003, Pages 1-78

  Talagrand, Michel ^a  

^a INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

Cavity method; p spin interaction model; Poisson Dirichlet distribution; Pure states; Replica symmetry breaking

Indexed keywords

EID: 0037340681     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X03001588     Document Type: Article

References (16)

1. M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, 1991.
2. M. Talagrand, Regularity of Gaussian processes, Acta. Math. 159 (1987), 99-149.
3. M. Mezard, G. Parisi and M. A. Virasiro, Spin Glass Theory and Beyond, World Scientific Lecture note in Physics, 9, World Scientific, 1987.
4. D. Sherrington and S. Kirkpatrick, Solvable model of a spin glass, Phys. Rev. Lett. 35 (1972), 1792-1796.
5. D. Gross and M. Mezard, The simplest spin glass, Nucl. Phys. B240 (1984), 431-452.
6. E. Gardner, Spin glasses with p-spin interactions, Nucl. Phys. B257 (1985), 747-765.
7. B. Derrida, Random-energy model: Limit of a family of disordered models, Phys. Rev. Lett. 45(2) (1980), 79-82.
8. M. Talagrand, Huge Random Structures and Mean Field Models for Spin Glasses, Proceedings of the International Congress of Mathematicians, Documenta. Math (electronic) special volume, 1998.
9. M. Talagrand, Rigorous Results for Mean Field Spin Glasses Models: A First Course, Saint Flour Summer school in Probability, August 2000, Springer Lectures Notes in Math., to appear.
10. M. Talagrand, Rigorous low temperature results for the mean field p-spins interaction model, Probab. Theory Relat. Fields 117 (2000), 303-360.
11. I. Ibragimov, V. Sudakov and B. Tsirelon, Norms of Gaussian sample functions, Proceedings of the third USSR-Japan symposium on Probability Theory, Lecture Note in math, Vol. 550, Springer Verlag, 1976.
12. M. Aizenmann and P. Contucci, On the stability of the quenched state in mean field spin glasses models, J. Stat. Phys. 92 (1998), 765-783.
13. S. Ghirlanda and F. Guerra, General properties of overlap distributions in disordered spin systems: Towards Parisi ultrametricity, J. Phys. A31 (1998), 9149-9155.
14. A. Ruelle, A mathematical reformulation of Derrida's REM and GREM, Comm. Math. Phys. 108 (1987), 225-239.
15. J. Pitmam and M. Yor, The two parameters Poisson Dirichlet distribution derived from a stable subordinator, Ann. Probab. 25 (1997), 855-900.
16. B. Derrida, Random energy model: An exactly solvable model of disordered systems, Phys. Rev. B24(5) (1981), 2613-2626.