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

TL;DR

This paper uses numerical transfer-matrix methods to analyze surface tension anisotropy in Ising models on square and cubic lattices, providing estimates consistent with prior studies but limited by computational size constraints.

Contribution

It applies transfer-matrix techniques to compute surface free energy, stiffness, and single-step free energy in Ising models, offering a different approach aligned with existing results.

Findings

Transfer-matrix estimates agree with previous series and Monte Carlo results.

Finite-size scaling of interfacial correlation length aids in analyzing surface properties.

Current computational limits restrict system sizes, limiting quantitative improvements.

Abstract

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.