A mean-field monomer-dimer model with random monomer activities. Exact solution and rigorous results

TL;DR

This paper provides an exact solution and rigorous analysis of a mean-field monomer-dimer model with random monomer activities, demonstrating self-averaging properties and deriving explicit formulas for dimer density.

Contribution

It introduces a solvable variational principle for the pressure density and computes the dimer density exactly in the thermodynamic limit for the first time.

Findings

Pressure density is self-averaging under general conditions.

Dimer density is a smooth function in the thermodynamic limit.

Exact formulas for dimer density are derived.

Abstract

Independent random monomer activities are considered on a mean-feld monomer-dimer model. Under very general conditions on the randomness the model is shown to have a self-averaging pressure density that obeys a solvable variational principle. The dimer density is exactly computed in the thermodynamic limit and shown to be a smooth function.