The nematic phase of a system of long hard rods

This paper [1] considers 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. The authors rigorously prove the existence of a nematic phase (shown to exist for rods of length k \ge 7 via numerical simulations [2]), i.e., they show 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: they first coarse grain the system on a scale comparable with the rods' length; then express the resulting effective theory as a contour model, which can be treated by Pirogov-Sinai methods [3].

References:
[1] M. Disertori and A. Giuliani, arXiv:1112.5564 (2012)
[2] A. Ghosh and D. Dhar, Europhysics Letters 78, 20003 (2007)
[3] R. Kotecky, Encyclopedia of Mathematical Physics, Elsevier, pp.60-65 (2006