Interacting double dimer model on the square lattice

TL;DR

This paper investigates the phase diagram of the square-lattice double dimer model, revealing a synchronization transition and novel phases, with implications for understanding coupled dimer systems.

Contribution

It introduces a symmetry-based analysis of an effective height theory showing infinitesimal coupling can synchronize the double dimer model, and maps out the full phase diagram including new phases.

Findings

Identified a phase transition from Coulomb to synchronized phase.

Discovered a novel antisynchronized phase with repulsive coupling.

Established the full phase diagram via Monte Carlo simulations.

Abstract

We study phases and transitions of the square-lattice double dimer model, consisting of two coupled replicas of the classical dimer model. As on the cubic lattice, we find a thermal phase transition from the Coulomb phase, a disordered but correlated dimer liquid, to a phase where fluctuations of the two replicas are closely synchronized with one another. Surprisingly, and in contrast to the cubic case, the phase boundary includes the noninteracting point, as we establish using a symmetry-based analysis of an effective height theory, indicating that infinitesimal coupling is sufficient to synchronize the double dimer model. In addition, we observe a novel antisynchronized phase when the coupling between replicas is repulsive, and use Monte Carlo simulations to establish the full phase diagram, including (anti)synchronized columnar and staggered phases, with interactions between parallel dimers in each replica.