# The columnar-disorder phase boundary in a mixture of hard squares and dimers

## TL;DR

This paper investigates the phase transition in a lattice model of hard squares and dimers, estimating the boundary between disordered and ordered phases using analytical methods that align well with simulations.

## Contribution

It introduces an analytical approach to estimate the phase boundary in a mixture of hard squares and dimers, validated by Monte Carlo simulations.

## Key findings

- Phase boundary estimates agree with simulations
- Identified a Kosterlitz-Thouless transition
- Characterized the nature of ordered and disordered phases

## Abstract

A mixture of hard squares, dimers and vacancies on a square lattice is known to undergo a transition from a low-density disordered phase to high-density columnar ordered phase. Along the fully packed square-dimer line, the system undergoes an Kosterliz-Thouless type transition to a phase with power law correlations. We estimate the phase boundary separating the ordered and disordered phases by calculating the interfacial tension between two differently ordered phases within two different approximation schemes. The analytically obtained phase boundary is in good agreement with Monte Carlo simulations.