A cluster expansion approach to the Heilmann-Lieb liquid crystal model

Abstract

A monomer-dimer model with a short-range attractive interaction favoring colinear dimers is considered on the lattice ${\mathbb{Z}}^2$. Although our choice of the chemical potentials results in more horizontal than vertical dimers, the horizontal dimers have no long-range traslational order - in agreement with the Heilmann-Lieb conjecture.

42 pages, 3 figures

References in corpus (1)

• Cluster expansion for abstract polymer models. New bounds from an old approach

Cited by in corpus (3)

• Nematic liquid crystal phase in a system of interacting dimers and monomers
• Two populations mean-field monomer-dimer model
• Finite-size corrections for the attractive mean-field monomer-dimer model