A 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 $\tau (T),$ 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.

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

References in corpus (3)

• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Properties of Interfaces in the two and three dimensional Ising Model
• Surface Tension, Surface Stiffness, and Surface Width of the 3-dimensional Ising Model on a Cubic Lattice

Cited by in corpus (10)

• Critical amplitudes and mass spectrum of the 2D Ising model in a magnetic field
• Monte Carlo Determination of Multiple Extremal Eigenpairs
• Study of the 2d Ising Model with mixed perturbation
• Modulation of Local Magnetization in two-dimensional Axial-Next-Nearest-Neighbor Ising model
• Resolving the two-dimensional ANNNI model using transfer matrices
• Interaction effects in the spectrum of the three-dimensional Ising model
• Order parameter of a three-dimensional Ising-like system in the simplest and higher non-Gaussian approximations
• Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices
• The interface tension in the improved Blume-Capel model
• Extrapolation-CAM Theory for Critical Exponents