Wetting and layering in the nearest-neighbor simple-cubic Ising lattice: A Monte Carlo investigation.

Abstract

Critical, tricritical, and first-order wetting transitions are studied in a simple-cubic nearest-neighbor Ising model, with exchange J in the bulk and exchange ${J}_{s}$ in the surface planes, by applying suitable bulk and surface fields H and ${H}_{1}$. Monte Carlo calculations are presented for systems of size L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}D, in a thin film geometry with D=40 layers and two free L\ifmmode\times\else\texttimes\fi{}L surfaces, with L ranging from L=10 to L=50. In addition, evidence for prewetting transitions and for layering transitions (the latter occur for temperatures T less than the roughening temperature ${T}_{R}$) is presented. We study the magnetization ${m}_{1}$ in the surface layer, susceptibilities ${\ensuremath{\chi}}_{11}$=\ensuremath{\partial}${m}_{1}$/\ensuremath{\partial}${H}_{1}$ and ${\ensuremath{\chi}}_{1}$=\ensuremath{\partial}${m}_{1}$/\ensuremath{\partial}H, surface excess magnetization ${m}_{s}$ and energy ${U}_{s}$, as well as magnetization and energy profiles [m(z) and U(z)] as a function of the distance z from the surface. We compare our results to various theoretical predictions; in particular, our results for critical wetting are consistent with simple mean-field behavior, the different singular behavior predicted by various renormalization-group treatments is not observed. We also analyze the qualitative structure of the full surface phase diagram of the model.