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

TL;DR

This paper rigorously proves the existence of a nematic phase in a two-dimensional lattice model of long hard rods, demonstrating orientational order without positional order at intermediate densities.

Contribution

It introduces a novel two-scales cluster expansion and Pirogov-Sinai analysis to establish nematic order in a lattice liquid crystal model.

Findings

Existence of a nematic phase with orientational order

No positional order at intermediate densities

Rigorous mathematical proof using cluster expansion and contour models

Abstract

In this talk I 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. I report a rigorous proof of the existence of a nematic phase: by this I mean 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: first the system is coarse-grained on a scale comparable with the rods' length; then the resulting effective theory is re-expressed as a contours' model, which can be treated by Pirogov-Sinai methods. The talk is based on joint work with Margherita Disertori.