A Numerical Transfer-Matrix Study of Surface-Tension Anisotropy in Ising Models on Square and Cubic Lattices

Details A Numerical Transfer-Matrix Study of Surface-Tension Anisotropy in Ising Models on Square and Cubic Lattices A Numerical Transfer-Matrix Study of Surface-Tension Anisotropy in Ising Models on Square and Cubic Lattices

1993-05-13

arxiv.org/abs/cond-mat/9305010v1

Phys. Rev. B, 48 (1993) 14584-14598

Physics

Condensed Matter

40 pages, 17 figures available on request. RevTeX version 2.1

Scientific paper

10.1103/PhysRevB.48.14584

We compute by numerical transfer-matrix methods the surface free energy $\tau(T),$ the surface stiffness coefficient $\kappa(T),$ and the single-step free energy $s(T)$ for Ising ferromagnets with $(\infty \times L)$ square-lattice and $(\infty \times L \times M)$ 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, either for rough or for smooth interfaces. The finite-size scaling behavior of the interfacial correlation length provides the means of investigating $\kappa(T)$ 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.

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