# Two populations mean-field monomer-dimer model

## TL;DR

This paper analyzes a two-population mean-field monomer-dimer model with interactions, deriving a variational principle for pressure density and identifying a ferromagnetic phase transition in a specific limit.

## Contribution

It introduces a novel two-population mean-field monomer-dimer model with both hard-core and attractive interactions, and characterizes its phase transition behavior.

## Key findings

- Pressure density satisfies a three-dimensional variational principle.
- A ferromagnetic phase transition is identified in a specific population size limit.
- The model extends understanding of monomer-dimer systems with multiple populations.

## Abstract

A two populations mean-field monomer-dimer model including both hard-core and attractive interactions between dimers is considered. The pressure density in the thermodynamic limit is proved to satisfy a three-dimensional variational principle. A detailed analysis is made in the limit in which one population is much smaller than the other and a ferromagnetic mean-field phase transition is found.