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 fS(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.
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Mon et al. (1989) studied this question.