Coulomb and Liquid Dimer Models in Three Dimensions

TL;DR

This paper investigates three-dimensional classical dimer models on various lattices, revealing critical Coulomb phases on bipartite lattices and confined phases on non-bipartite lattices through analytical and simulation methods.

Contribution

It extends the understanding of dimer models to three dimensions, demonstrating the existence of critical Coulomb phases only on bipartite lattices using analytical and Monte Carlo approaches.

Findings

Coulomb phase with algebraic correlations on bipartite cubic lattice

Confined and exponentially deconfined phases on non-bipartite lattices

Extended critical phases are exclusive to bipartite lattices in higher dimensions

Abstract

We study classical hard-core dimer models on three-dimensional lattices using analytical approaches and Monte Carlo simulations. On the bipartite cubic lattice, a local gauge field generalization of the height representation used on the square lattice predicts that the dimers are in a critical Coulomb phase with algebraic, dipolar, correlations, in excellent agreement with our large-scale Monte Carlo simulations. The non-bipartite FCC and Fisher lattices lack such a representation, and we find that these models have both confined and exponentially deconfined but no critical phases. We conjecture that extended critical phases are realized only on bipartite lattices, even in higher dimensions.