Monte Carlo studies of anisotropic surface tension and interfacial roughening in the three-dimensional Ising model

Extensive Monte Carlo simulations of the simple cubic Ising model with nearest-neighbor ferromagnetic interactions with a tilted interface are presented for a wide range of lattice size L, temperature T, and tilt angles θ. The anisotropic interfacial tension is studied in detail. From the small-angle data, we obtain the step free energy density $f_S$(T,L). Finite-size scaling of the step free energy density is discussed and used to probe the predicted temperature dependence of the correlation length near and above the roughening transition. The square-root temperature dependence predicted by solid-on-solid model calculations is exhibited. Finite-size scaling implies that the step free energy varies as 1/L in the rough phase, and thus the applicability of a capillary wave Hamiltonian to describe interfaces of lattice models needs careful discussion.