Determination of the Critical Exponents for the Isotropic-Nematic Phase Transition in a System of Long Rods on Two-dimensional Lattices: Universality of the Transition

TL;DR

This study uses Monte Carlo simulations and finite-size scaling to determine the critical exponents of the isotropic-nematic phase transition in long rods on 2D lattices, confirming universality classes for different lattice types.

Contribution

It provides the first detailed analysis of the critical behavior and universality classes of the isotropic-nematic transition for long rods on 2D lattices.

Findings

Transition belongs to 2D Ising universality class on square lattices.

Transition belongs to three-state Potts universality class on triangular lattices.

Critical exponents are determined through finite-size scaling analysis.

Abstract

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior and universality for the isotropic-nematic phase transition in a system of long straight rigid rods of length $k$ ($k$-mers) on two-dimensional lattices. The nematic phase, characterized by a big domain of parallel $k$-mers, is separated from the isotropic state by a continuous transition occurring at a finite density. The determination of the critical exponents, along with the behavior of Binder cumulants, indicate that the transition belongs to the 2D Ising universality class for square lattices and the three-state Potts universality class for triangular lattices.