Monte Carlo investigation of critical properties of the Landau point of a biaxial liquid-crystal system

Abstract

Extensive Monte Carlo simulations are performed to investigate the critical properties of a special singular point usually known as the Landau point. The singular behavior is studied in the case when the order parameter is a tensor of rank 2. Such an order parameter is associated with a nematic-liquid-crystal phase. A three-dimensional lattice dispersion model that exhibits a direct biaxial nematic-to-isotropic phase transition at the Landau point is thus chosen for the present study. Finite-size scaling and cumulant methods are used to obtain precise values of the critical exponent ν = 0.713(4), the ratio γ/ν = 1.85(1), and the fourth-order critical Binder cumulant U ∗ = 0.6360(1). Estimated values of the exponents are in good agreement with renormalization-group predictions.