Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Cavity method in the spherical SK model

Dmitry Panchenko

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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.

Résumé

Nous développons la méthode de la cavité pour le modèle sphérique de Sherrington–Kirkpatrick à haute température et champs externe faible. Nous illustrons la méthode par le calcul de la matrice de covariance des fluctuations des recouvrements et de la magnétisation.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 45, Number 4 (2009), 1020-1047.

Dates
First available in Project Euclid: 6 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1257529890

Digital Object Identifier
doi:10.1214/08-AIHP193

Mathematical Reviews number (MathSciNet)
MR2572162

Zentralblatt MATH identifier
1193.82021

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)

Keywords
Sherrington–Kirkpatrick model Cavity method

Citation

Panchenko, Dmitry. Cavity method in the spherical SK model. Ann. Inst. H. Poincaré Probab. Statist. 45 (2009), no. 4, 1020--1047. doi:10.1214/08-AIHP193. https://projecteuclid.org/euclid.aihp/1257529890


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References

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