Interacting dimers on the simple cubic lattice as a model for liquid crystals

Abstract

The authors consider two lattice gas models where dimers are placed on the simple cubic lattice with an attractive interaction between collinear dimers. They prove (using reflection positivity and Peierls' argument) that at low enough temperatures both models exist in an ordered state where one or two of the three orientations are preferred. No attempt is made at deciding whether the ordered state actually has dimers of two orientations or only of one orientation. Both models have earlier been considered in the two-dimensional version and proved to exhibit ordering at low temperature.