Higher order expansions for the overlap of the SK model

2002/11/27 by X. Bardina, Bardina, X., D. Marquez-Carreras +5
Mathematics · #60G15 #60G60 #82A87 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G15 #msc:60G60 #msc:82A87

paper · pdf · doi:10.48550/arxiv.math/0211422

arxiv created 2002/11/27 · arxiv updated 2009/11/30

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.

Related

• The expansion for the overlap function
• On the phase diagram of the multiscale mean-field spin-glass
• High temperature Sherrington-Kirkpatrick model for general spins
• A central limit theorem for a localized version of the SK model
• Central Limit Theorem of Overlap for the Mean Field Ghatak-Sherrington model