Gauge theory picture of an ordering transition in a dimer model

TL;DR

This paper investigates a phase transition in a 3D lattice gauge theory derived from a classical dimer model, revealing a continuous transition characterized by a Higgs mechanism and duality to an XY model with geometric frustration.

Contribution

It introduces a gauge theory framework for the dimer model transition and provides numerical evidence for a continuous transition with unique critical exponents.

Findings

Transition is continuous with exponents close to 3D XY model

Duality relates the dimer model to an XY gauge theory

Flowgram analysis confirms the transition's continuous nature

Abstract

We study a phase transition in a 3D lattice gauge theory, a "coarse-grained" version of a classical dimer model. Duality arguments indicate that the dimer lattice theory should be dual to a XY model coupled to a gauge field with geometric frustration. The transition between a Coulomb phase with dipolar correlations and a long range ordered columnar phase is understood in terms of a Higgs mechanism. Monte Carlo simulations of the dual model indicate a continuous transition with exponents close but apparently different from those of the 3d XY model. The continuous nature of the transition is confirmed by a flowgram analysis.