The nematic-disordered phase transition in systems of long rigid rods on two dimensional lattices

TL;DR

This study investigates the phase transition from nematic to disordered phases in systems of long rigid rods on 2D lattices, revealing continuous transitions and critical behaviors that differ from classical models.

Contribution

It provides new insights into the nature of phase transitions in long rigid rod systems, including evidence for universality classes and correlation length scales.

Findings

Continuous phase transition observed for rods of length 7.

Evidence of a crossover length scale around 1400 lattice units.

Critical exponents differ from Ising model but align with three-state Potts model on triangular lattice.

Abstract

We study the phase transition from a nematic phase to a high-density disordered phase in systems of long rigid rods of length $k$ on the square and triangular lattices. We use an efficient Monte Carlo scheme that partly overcomes the problem of very large relaxation times of nearly jammed configurations. The existence of a continuous transition is observed on both lattices for $k=7$. We study correlations in the high-density disordered phase, and we find evidence of a crossover length scale $\xi^* \gtrsim 1400$, on the square lattice. For distances smaller than $\xi^*$, correlations appear to decay algebraically. Our best estimates of the critical exponents differ from those of the Ising model, but we cannot rule out a crossover to Ising universality class at length scales $\gg \xi^*$. On the triangular lattice, the critical exponents are consistent with those of the two dimensional three-state Potts universality class.