Phase diagram of a biaxial nematogenic lattice model: A Monte Carlo simulation study

TL;DR

This study uses Monte Carlo simulations to map the phase diagram of biaxial nematic molecules, confirming the existence of uniaxial and biaxial phases and identifying a tricritical point, with results aligning qualitatively with mean-field predictions.

Contribution

First Monte Carlo simulation of the biaxial nematic lattice model confirming phase types and tricritical point predicted by mean-field theory.

Findings

Confirmed uniaxial and biaxial nematic phases

Identified a tricritical point in the phase transition

Located the triple point differently from theoretical predictions

Abstract

The phase diagram for a lattice system of biaxial molecules possessing $D_{2h}$ symmetry and interacting with Straley's quadrupolar pair potential in Sonnet-Virga-Durand parameterization [A. M. Sonnet, E. G. Virga, and G. E. Durand, Phys. Rev. E {\bf67}, 061701 (2003)] has been determined using Monte Carlo simulation. Our results confirm that the nematogenic model yields both the uniaxial and biaxial nematic macroscopic phases along with a tricritical point in the transition from uniaxial to biaxial nematics as predicted in mean field theory. By analyzing the behavior of a free-energy-like function, derived from the probability distributions of energy, the order of phase transitions is detected. A conclusive numerical evidence in support of the existence of a tricritical point on the uniaxial-biaxial transition line in the phase diagram is reported. Although the nature of the phase diagram is qualitatively identical as obtained in the mean-field study however the location of the triple point differs significantly from theoretical prediction.