Numerical transfer-matrix study of surface-tension anisotropy in Ising models on square and cubic lattices

We compute by numerical transfer-matrix methods the surface free energy τ(T), the surface stiffness coefficient κ(T), and the step free energy s(T) for Ising ferromagnets with (∞×L) square-lattice and (∞×L×M) cubic-lattice geometries, into which an interface is introduced by imposing antiperiodic or plus/minus boundary conditions in one transverse direction. These quantities occur in expansions of the angle-dependent surface tension for either rough or smooth interfaces. The finite-size scaling behavior of the interfacial correlation length provides the means of investigating τ(T), κ(T), and s(T). The resulting transfer-matrix estimates are fully consistent with previous series and Monte Carlo studies, although current computational technology does not permit transfer-matrix studies of sufficiently large systems to show quantitative improvement over the previous estimates.