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In this talk I consider a two-dimensional lattice model for liquid crystalsconsisting of long rods interacting via purely hard core interactions, with twoallowed orientations defined by the underlying lattice. I report a rigorousproof of the existence of a nematic phase: by this I mean that at intermediatedensities the system exhibits orientational order, either horizontal orvertical, but no positional order. The proof is based on a two-scales clusterexpansion: first the system is coarse-grained on a scale comparable with therods' length; then the resulting effective theory is re-expressed as acontours' model, which can be treated by Pirogov-Sinai methods. The talk isbased on joint work with Margherita Disertori.

The nematic phase of a system of long hard rods - ICMP12 talk, Aalborg, August 2012