Surface Tension, Surface Stiffness, and Surface Width of the 3-dimensional Ising Model on a Cubic Lattice

TL;DR

This study investigates the interface properties of the 3D Ising model across various temperatures, providing detailed measurements of surface tension, stiffness, and width using efficient algorithms and large lattices.

Contribution

It offers comprehensive numerical analysis of interface phenomena in the 3D Ising model, including new data on surface tension, stiffness, and width over a wide temperature range.

Findings

Interface tension sigma computed across temperatures.

Large distance behavior matches massless Gaussian dynamics.

Universal quantities like xi^2 * sigma are analyzed.

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 sigma is obtained by integrating the surface energy density over the inverse temperature beta. We use lattices of size L x L x 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 that 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 kappa is determined. We also attempt to determine the correlation length xi and study universal quantities like xi^2 * sigma and xi^2 * kappa. Results for the interfacial width on lattices up to 512 x 512 x 27 are also presented.