Higher order expansions for the overlap of the SK model

Xavier Bardina, David Màrquez-Carreras, Carles Rovira and Samy Tindel.

Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007-Barcelona, Spain
Département de Mathématiques, Institut Galilée - Université Paris 13,  Avenue  J. B. Clément, 93430-Villetaneuse, France.

Abstract

In this note, the Sherrington Kirkpatrick model of interacting spins is under consideration. In the high temperature region, we give an asymptotic expansion for the expected value of some genereral polynomial of the overlap of the system when the size $N$ grows to infinity. Some of the coefficients obtained are shown to be vanishing, while the procedure to get the nontrivial ones has to be performed by a computer program, due to the great amount of computation involved.
 
Published in: Proceedings Ascona. Progress in Probability. Birkhäuser, 58, 21-43, 2004