We present the results of extensive Monte Carlo simulations of phase transitions and critical behavior at the surface of a simple cubic Ising model. Profiles of the magnetization and internal energy are determined as a function of the distance from the surface, and we extract surface and bulk properties as a function of temperature and surface coupling
Js. The surface-bulk multicritical point is located with improved precision,
Js/J=1.52\ifmmode\pm\else\textpm\fi{}0.02, and crossover behavior is studied. New estimates for critical exponents are extracted, ${\ensuremath{\gamma}}_{1}$=0.78\ifmmode\pm\else\textpm\fi{}0.06, ${\ensuremath{\gamma}}_{1}^{\mathit{m}}$=1.41\ifmmode\pm\else\textpm\fi{}0.14, ${\ensuremath{\gamma}}_{11}^{\mathit{m}}$=0.96\ifmmode\pm\else\textpm\fi{}0.09, and along with critical amplitude ratios these are compared with theoretically predicted values.
Monte Carlo simulations have been performed to investigate the equilibrium phase behaviour of a transverse Ising model in a thin-film geometry under the action of competing surface fields. This model is a classical isotropic vector spin model with a ferromagnetic Ising Hamiltonian and a transverse field applied perpendicular to the Ising z-axis. For finite values of the transverse field strength, , the model displays an interface localization transition with a spontaneous magnetization of the film below a critical temperature Tc. However, in the limit , no spontaneous magnetization of the film is observed. In the two-phase regime, below Tc, a degeneracy exists in the magnetization profiles across the film between states of positive and negative total magnetization. The interface localization transition temperature lies below the bulk critical temperature of the film for competing surface fields.