Phase diagram of an extended classical dimer model

TL;DR

This study explores the phase transitions in a three-dimensional extended classical dimer model, revealing conditions for continuous and first-order transitions and identifying a tricritical point through extensive Monte Carlo simulations.

Contribution

It provides the first detailed phase diagram of a generalized dimer model with plaquette and cubic interactions, highlighting the nature of phase transitions and the existence of a tricritical point.

Findings

Continuous transition with critical exponent η ~ 0.2 when interactions compete.

First-order transition when both interactions favor alignment.

Discovery of a highly-degenerate crystalline phase at low temperature.

Abstract

We present an extensive numerical study of the critical behavior of dimer models in three dimensions, focusing on the phase transition between Coulomb and crystalline columnar phases. The case of attractive interactions between parallel dimers on a plaquette was shown to undergo a continuous phase transition with critical exponents close to those of the O(N) tricritical universality class, a situation which is not easily captured by conventional field theories. That the dimer model is exactly fine-tuned to a highly symmetric point is a non trivial statement which needs careful numerical investigation. In this paper, we perform an extensive Monte Carlo study of a generalized dimer model with plaquette and cubic interactions and determine its extended phase diagram. We find that when both interactions favor alignment of the dimers, the phase transition is first order, in almost all cases. On the opposite, when interactions compete, the transition becomes continuous, with a critical exponent \eta ~ 0.2. The existence of a tricritical point between the two regimes is confirmed by simulations on very large size systems and a flowgram method. In addition, we find a highly-degenerate crystalline phase at very low temperature in the frustrated regime which is separated from the columnar phase by a first order transition.