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 single-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. The surface tension σ(θ, T ) per unit length of interface projected in the longitudinal direction defines τ(T ) and κ(T ) for temperatures at which the interface is rough: σ(θ, T )/cos θ = τ(T ) + 1 2κ(T )θ 2 + O(θ4). For temperatures at which the interface is smooth, s(T ) is the free-energy contribution of the dominant entropy-producing fluctuation, a single-step terrace. The finite-size scaling behavior of the interfacial correlation length provides the means of investigating κ(T ) and s(T ). The resulting transfer-matrix estimates are fully consistent with previous series and Monte Carlo studies, although current computational tech-