Cavity method in the spherical SK model

Dmitry Panchenko

Annales de l'I.H.P. Probabilités et statistiques (2009)

  • Volume: 45, Issue: 4, page 1020-1047
  • ISSN: 0246-0203

Abstract

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We develop a cavity method for the spherical Sherrington–Kirkpatrick model at high temperature and small external field. As one application we compute the limit of the covariance matrix for fluctuations of the overlap and magnetization.

How to cite

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Panchenko, Dmitry. "Cavity method in the spherical SK model." Annales de l'I.H.P. Probabilités et statistiques 45.4 (2009): 1020-1047. <http://eudml.org/doc/78051>.

@article{Panchenko2009,
abstract = {We develop a cavity method for the spherical Sherrington–Kirkpatrick model at high temperature and small external field. As one application we compute the limit of the covariance matrix for fluctuations of the overlap and magnetization.},
author = {Panchenko, Dmitry},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Sherrington–Kirkpatrick model; cavity method; Sherrington-Kirkpatrick model},
language = {eng},
number = {4},
pages = {1020-1047},
publisher = {Gauthier-Villars},
title = {Cavity method in the spherical SK model},
url = {http://eudml.org/doc/78051},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Panchenko, Dmitry
TI - Cavity method in the spherical SK model
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2009
PB - Gauthier-Villars
VL - 45
IS - 4
SP - 1020
EP - 1047
AB - We develop a cavity method for the spherical Sherrington–Kirkpatrick model at high temperature and small external field. As one application we compute the limit of the covariance matrix for fluctuations of the overlap and magnetization.
LA - eng
KW - Sherrington–Kirkpatrick model; cavity method; Sherrington-Kirkpatrick model
UR - http://eudml.org/doc/78051
ER -

References

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  1. [1] Crisanti, A. and Sommers, H. J.The spherical p-spin interaction spin glass model: The statics. Z. Phys. B. Condensed Matter 83 (1992) 341–354. 
  2. [2] Guerra, F. and Toninelli, F. L.Central limit theorem for fluctuations in the high temperature region of the Sherrington–Kirkpatrick spin glass model. J. Math. Phys. 43 (2002) 6224–6237. Zbl1060.82024MR1939641
  3. [3] Sherrington, D. and Kirkpatrick, S.Solvable model of a spin glass. Phys. Rev. Lett. 35 (1975) 1792–1796. 
  4. [4] Talagrand, M.Replica symmetry breaking and exponential inequalities for the Sherrington–Kirkpatrick model. Ann. Probab. 28 (2000) 1018–1062. Zbl1034.82027MR1797303
  5. [5] Talagrand, M.Spin Glasses: A Challenge for Mathematicians. Cavity and Mean Field Models. Springer, Berlin, 2003. Zbl1033.82002MR1993891
  6. [6] Talagrand, M.Free energy of the spherical mean field model. Probab. Theory Related Fields 134 (2006) 339–382. Zbl1130.82019MR2226885
  7. [7] Talagrand, M.Large deviations, Guerra’s and A.S.S. schemes, and the Parisi hypothesis. J. Stat. Phys. 126 (2007) 837–894. Zbl1133.82330MR2311888

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