Criticality of a classical dimer model on the triangular lattice

TL;DR

This paper investigates a classical dimer model on the triangular lattice, revealing a sequence of phases including disordered, critical, and ordered states, challenging the belief that criticality is exclusive to bipartite lattices.

Contribution

It demonstrates the existence of a critical phase in a non-bipartite triangular lattice dimer model, contrary to previous assumptions.

Findings

Disordered liquid phase at low interactions

Critical phase similar to square lattice case

First order transition to ordered phase in isotropic case

Abstract

We consider a classical interacting dimer model which interpolates between the square lattice case and the triangular lattice case by tuning a chemical potential in the diagonal bonds. The interaction energy simply corresponds to the number of plaquettes with parallel dimers. Using transfer matrix calculations, we find in the anisotropic triangular case a succession of different physical phases as the interaction strength is increased: a short range disordered liquid dimer phase at low interactions, then a critical phase similar to the one found for the square lattice, and finally a transition to an ordered columnar phase for large interactions. The existence of the critical phase is in contrast with the belief that criticality for dimer models is ascribed to bipartiteness. For the isotropic triangular case, we have indications that the system undergoes a first order phase transition to an ordered phase, without appearance of an intermediate critical phase.