A mechanical approach to mean field spin models

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 detail 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.