Dimensional crossover in the anisotropic 3D Ising model: a Monte Carlo study

A Monte Carlo simulation and a finite-size sealing were employed to study the dimensional crossover in the anisotropic 3D Isling model. In contrast to a previous report, there was no thermal hysteresis. The effective critical temperature defined by the temperature of maximum susceptibility showed a drastic finite-size effect. The critical temperature followed the crossover scaling relation with the crossover exponent phi = 1.49, which is inconsistent with the theoretical expectation phi = gamma = 7/4. The critical exponent v(2) for the correlation length along the anisotropic direction varied between 0.625 (3D limit) and 0 (2D limit). The dimensional crossover corresponded to the crossover from an isotropic to an anisotropic growth of the correlation length.