Monte Carlo study of surface phase transitions in the three-dimensional Ising model.

Abstract

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 ${\mathit{J}}_{\mathit{s}}$. The surface-bulk multicritical point is located with improved precision, ${\mathit{J}}_{\mathit{s}}$/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.