Pocket Monte Carlo algorithm for classical doped dimer models

TL;DR

This paper introduces an efficient Monte Carlo cluster algorithm for classical doped dimer models, revealing how doping affects monomer correlations and confinement in different lattice geometries.

Contribution

The paper presents a novel, scalable cluster algorithm applicable to various dimensions and lattices for studying doped dimer models.

Findings

Doping destroys the critical confinement in the square lattice dimer model.

Monomers form a screened Coulomb plasma at finite doping.

On the triangular lattice, monomers are not confined and correlations are short-ranged.

Abstract

We study the correlations of classical hardcore dimer models doped with monomers by Monte Carlo simulation. We introduce an efficient cluster algorithm, which is applicable in any dimension, for different lattices and arbitrary doping. We use this algorithm for the dimer model on the square lattice, where a finite density of monomers destroys the critical confinement of the two-monomer problem. The monomers form a two-component plasma located in its high-temperature phase, with the Coulomb interaction screened at finite densities. On the triangular lattice, a single pair of monomers is not confined. The monomer correlations are extremely short-ranged and hardly change with doping.