A mechanical approach to mean field spin models
Mathematical Physics
2015-05-13 v2 math.MP
Abstract
Inspired by the bridge pioneered by Guerra among statistical mechanics on lattice and analytical mechanics on 1+1 continuous Euclidean space-time, we built a self-consistent method to solve for the thermodynamics of mean-field models defined on lattice, whose order parameters self average. We show the whole procedure by analyzing in full details the simplest test case, namely the Curie-Weiss model. Further we report some applications also to models whose order parameters do not self-average, by using the Sherrington-Kirkpatrick spin glass as a guide.
Keywords
Cite
@article{arxiv.0812.1978,
title = {A mechanical approach to mean field spin models},
author = {Giuseppe Genovese and Adriano Barra},
journal= {arXiv preprint arXiv:0812.1978},
year = {2015}
}