# Synchronization transition in the double dimer model on the cubic lattice

## TL;DR

This paper investigates a classical cubic-lattice double dimer model, revealing a continuous synchronization transition with strong correlations between replicas, characterized by a novel universality class, and explores the phase diagram with additional interactions.

## Contribution

It introduces the concept of a synchronization transition in coupled dimer models, characterizes its universality class, and provides an exact Bethe lattice solution that captures the qualitative phase structure.

## Key findings

- Identifies a continuous synchronization transition without symmetry breaking.
- Classifies the transition within the 3D inverted-XY universality class.
- Provides an exact Bethe lattice solution that reproduces the phase diagram qualitatively.

## Abstract

We study the classical cubic-lattice double dimer model, consisting of two coupled replicas of the close-packed dimer model, using a combination of theoretical arguments and Monte Carlo simulations. Our results establish the presence of a 'synchronization transition' at a critical value of the coupling, where both replicas remain disordered but their fluctuations become strongly correlated. We show that this unconventional transition, which has neither external nor spontaneous symmetry breaking, is continuous and belongs to the 3D inverted-XY universality class. By adding aligning interactions for dimers within each replica, we map out the full phase diagram including the interplay between columnar ordering and synchronization. We also solve the coupled double dimer model exactly on the Bethe lattice and show that it correctly reproduces the qualitative phase structure, but with mean-field critical behavior.