Nematic liquid crystal phase in a system of interacting dimers and monomers
Mathematical Physics
2018-09-26 v2 Statistical Mechanics
math.MP
Probability
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.
Keywords
Cite
@article{arxiv.1709.05297,
title = {Nematic liquid crystal phase in a system of interacting dimers and monomers},
author = {Ian Jauslin and Elliott H. Lieb},
journal= {arXiv preprint arXiv:1709.05297},
year = {2018}
}