Entropy-driven phase transition in a polydisperse hard-rods lattice system
概率论
2011-08-25 v1 数学物理
组合数学
math.MP
摘要
We study a system of rods on the 2d square lattice, with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N=2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals.
关键词
引用
@article{arxiv.math/0503222,
title = {Entropy-driven phase transition in a polydisperse hard-rods lattice system},
author = {Dmitry Ioffe and Yvan Velenik and Milos Zahradnik},
journal= {arXiv preprint arXiv:math/0503222},
year = {2011}
}