# Low-temperature behavior of the multicomponent Widom-Rowlison model on finite square lattices

## TL;DR

This paper investigates the low-temperature dynamics of a multicomponent particle system on finite square lattices, focusing on transition times between dominant configurations and how these depend on boundary conditions and lattice size.

## Contribution

It introduces a new combinatorial method to analyze transition times in the Widom-Rowlinson model on finite lattices, revealing the influence of boundary conditions and lattice dimensions.

## Key findings

- Identified the timescale for transitions between maximum-occupancy configurations.
- Showed how boundary conditions affect the transition times.
- Developed a novel combinatorial approach based on geometrical properties.

## Abstract

We consider the multicomponent Widom-Rowlison with Metropolis dynamics, which describes the evolution of a particle system where $M$ different types of particles interact subject to certain hard-core constraints. Focusing on the scenario where the spatial structure is modeled by finite square lattices, we study the asymptotic behavior of this interacting particle system in the low-temperature regime, analyzing the tunneling times between its $M$ maximum-occupancy configurations, and the mixing time of the corresponding Markov chain. In particular, we develop a novel combinatorial method that, exploiting geometrical properties of the Widom-Rowlinson configurations on finite square lattices, leads to the identification of the timescale at which transitions between maximum-occupancy configurations occur and shows how this depends on the chosen boundary conditions and the square lattice dimensions.