  In this talk I consider a two-dimensional lattice model for liquid crystals
consisting of long rods interacting via purely hard core interactions, with two
allowed orientations defined by the underlying lattice. I report a rigorous
proof of the existence of a nematic phase: by this I mean that at intermediate
densities the system exhibits orientational order, either horizontal or
vertical, but no positional order. The proof is based on a two-scales cluster
expansion: first the system is coarse-grained on a scale comparable with the
rods' length; then the resulting effective theory is re-expressed as a
contours' model, which can be treated by Pirogov-Sinai methods. The talk is
based on joint work with Margherita Disertori.
