Nematic liquid crystal phase in a system of interacting dimers and monomers

TL;DR

This paper proves the existence of a nematic liquid crystal phase in a monomer-dimer system with strong attractive interactions, confirming a longstanding conjecture by Heilmann and Lieb.

Contribution

It provides a rigorous proof of the nematic phase in a dimer model using Pirogov-Sinai theory and cluster expansion techniques.

Findings

Nematic phase occurs at large dimer activity and strong interactions.

Dimers predominantly align without translational order.

The model is mapped to a polymer system for analysis.

Abstract

We consider a monomer-dimer system with a strong attractive dimer-dimer interaction that favors alignment. In 1979, Heilmann and Lieb conjectured that this model should exhibit a nematic liquid crystal phase, in which the dimers are mostly aligned, but do not manifest any translational order. We prove this conjecture for large dimer activity and strong interactions. The proof follows a Pirogov-Sinai scheme, in which we map the dimer model to a system of hard-core polymers whose partition function is computed using a convergent cluster expansion.