We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.
@article{arxiv.0805.3698,
title = {SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model},
author = {Stephen Powell and J. T. Chalker},
journal= {arXiv preprint arXiv:0805.3698},
year = {2008}
}