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

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×L×D, in a thin film geometry with D=40 layers and two free L×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 ${\chi }_{11}$=∂$m_1$/∂$H_1$ and ${\chi }_1$=∂$m_1$/∂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.