Limit theorems for monomer-dimer mean-field models with attractive potential

TL;DR

This paper investigates the fluctuation behavior of monomers in a mean-field monomer-dimer model with attractive potential, revealing different statistical regimes at and near the critical point.

Contribution

It establishes limit theorems for monomer fluctuations and characterizes phase coexistence and universality classes at criticality.

Findings

Monomer fluctuations follow a central limit theorem outside the critical curve.

At the critical point, the model shares universality with mean-field ferromagnets.

Phase coexistence occurs along the critical curve.

Abstract

The number of monomers, in a monomer-dimer mean-field model with an attractive potential, fluctuates according to the central limit theorem when the parameters are outside the critical curve. At the critical point the model belongs to the same universality class of the mean-field ferromagnet. Along the critical curve the monomer and dimer phases coexist.