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

Abstract

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 2 κ(T )θ 2 + O(θ 4 ). 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-

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“…Since references [15,16] dealt with phenomena for β > β * c , we have only a few points δ 5 (β) with β < β * c (see figure 5). We use cubic splines to evaluate both δ L (β) and the first dδ L /dβ as continuous functions.…”

“…The authors wish to thank Professor M Kaburagi and Professor H Nishimori for useful comments and for the use of their programs KOBEPACK and TITPACK, respectively. The data for the three-dimensional Ising model were taken at Florida State University; consult reference [16] for details. The authors thank Professor Per Arne Rikvold for comments on the manuscript.…”

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