Rigorous Results on the Bipartite Mean-Field Model

TL;DR

This paper provides exact solutions for a bipartite mean-field model, analyzing phase transitions and critical points by computing the thermodynamic limit and examining the pressure functional under varying external fields.

Contribution

It introduces a rigorous method to compute the thermodynamic limit of a bipartite mean-field model with different interaction parameters and external fields.

Findings

Exact thermodynamic limit derived for the bipartite model

Critical points of the pressure functional identified

Behavior analyzed under different external field conditions

Abstract

We consider a bipartite mean-field model in which both the interaction constant and the external field take different values only depending on the groups particles belong to. We compute the exact value of the thermodynamic limit of the model exploiting a tail estimation on the number of configurations that share the same value of the magnetization and we analyze the critical points of the pressure functional associated to the symmetric version of the model as the external field is away or small.