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

摘要

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 nu = 0.713( 4), the ratio gamma/v = 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.