Surface tension, surface stiffness, and surface width of the 3-dimensional Ising model on a cubic lattice

Abstract

We compute properties of the interface of the 3-dimensional Ising model for a wide range of temperatures, covering the whole region from the low temperature domain through the roughening transition to the bulk critical point. The interface tension σ is obtained by integrating the surface energy density over the inverse temperature β. We use lattices of size L × L × T, with L up to 64, and T up to 27. The simulations with antiperiodic boundary conditions in T-direction are done with the Hasenbusch-Meyer interface cluster algorithm, which turns out to be very efficient. We demonstrate that in the rough phase the large distance behavior of the interface is well described by a massless Gaussian dynamics. The surface stiffness coefficient ϰ is determined. We also attempt to determine the correlation length ξ and study universal quantities like ξ 2σ and ξ 2ϰ. Results for the interfacial width on lattices up to 512 × 512 × 27 are also presented.