Diego Alberici — Università di Bologna #
Liquid crystals: a cluster expansion approach to the Heilmann-Lieb conjecture #
 Heilmann and Lieb (J.Stat.Phys. 1979) proposed a monomer-dimer model on the square lattice in order to describe a liquid crystal. They proved the existence of a long range orientational order induced by a short-range attractive intraction favoring colinear dimers. On the other hand they conjectured the absence of a complete translational order in the system. This conjecture is still open. In this talk I will show how cluster expansion methods have been recently used (J.Stat.Phys. 2016) to prove the absence of translational order in a modified system. In the future this approach could be extended to study the original problem.