Polydispersed rods on the square lattice

TL;DR

This paper analyzes the phase transition behavior of polydispersed rods on a square lattice, revealing a single transition from isotropic to nematic phase with Ising universality, differing from monodispersed systems.

Contribution

It provides the first grand-canonical solution for polydispersed rods on a lattice, identifying the critical line and universality class.

Findings

Single isotropic-nematic transition identified

No second transition at high density in polydispersed case

Critical exponents match Ising universality class

Abstract

We study the grand-canonical solution of a system of hard polydispersed rods placed on the square lattice using transfer matrix and finite size scaling calculations. We determine the critical line separating an isotropic from a nematic phase. No second transition to a disordered phase is found at high density, contrary to what is observed in the monodispersed case. The estimates of critical exponents and the central charge on the critical line are consistent with the Ising universality class.