A Cluster Expansion Approach to the Heilmann–Lieb Liquid Crystal Model

A monomer-dimer model with a short-range attractive interaction favoring collinear dimers is considered on the lattice Z2. Although our choice of the chemical potentials results in more horizontal than vertical dimers, the horizontal dimers have no long-range translational order—in agreement with the Heilmann–Lieb conjecture (Heilmann and Lieb in J Stat Phys 20(6):679–693, 1979).