1112.5564 (Margherita Disertori et al.)

The nematic phase of a system of long hard rods    [PDF]

Margherita Disertori, Alessandro Giuliani

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.

View original: http://arxiv.org/abs/1112.5564