A mechanical approach to mean field spin models

TL;DR

This paper introduces a mechanical approach to analyze mean-field spin models, providing a self-consistent method to determine their thermodynamics, demonstrated through the Curie-Weiss and Sherrington-Kirkpatrick models.

Contribution

It develops a novel mechanical framework for solving mean-field spin models, bridging statistical mechanics and analytical mechanics, with detailed analysis and applications.

Findings

Successfully applied to the Curie-Weiss model

Extended to spin glass models like Sherrington-Kirkpatrick

Provides a new self-consistent solution method for thermodynamics

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.