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.

Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density

“…The phases meet at the bicritical Landau point at A = B = 0, where the IN transition is second order [52,53]. A detailed characterization of a biaxial LC near the Landau point can be found in [85], where the critical exponents are calculated using a 3D lattice model with a Lebwohl-Lasher potential [86].…”

Dynamical phase transitions in generalized Kuramoto model with distributed Sakaguchi phase

“…where the brackets denote averaging over the ensemble of initial configurations. After its introduction and development [127] it has turned out to be a widely used tool to identify the nature of phase transitions in a variety of circumstances ranging from model magnetic systems [128][129][130][131], liquid crystals [132], foams [133], flocking systems [134] and opinion dynamics [135] to quantum chromodynamics [136]. This quantity U 4 detects the order of a phase transition in the following way [127,128]: (i) in a phase with a nonzero order parameter value, but with very small order parameter fluctuation, |Z| 4 ≈ |Z| 2 2 and so it attains the value 2 3 ; while in a completely disordered phase, it takes the value 0 and (ii) during a first order (discontinuous transition) transition, it shows a sharp jump to a very sharp minimum of a large negative value while for a second order (discontinuous) transition, it decreases from 2 3 but remains positive.…”