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