The nematic phase of a system of long hard rods

Details The nematic phase of a system of long hard rods The nematic phase of a system of long hard rods

2011-12-23

arxiv.org/abs/1112.5564v2

Physics

Mathematical Physics

36 pages, 4 figures; abstract changed, references added, comparison with literature improved, figures added

Scientific paper

We 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. We rigorously prove the existence of a nematic phase, i.e., we 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: we first coarse grain the system on a scale comparable with the rods' length; then we express the resulting effective theory as a contour's model, which can be treated by Pirogov-Sinai methods.

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