The Interface Tension of the 3-Dimensional Ising Model in the Scaling Region

TL;DR

This work numerically determines the interface free energy and tension in the 3D Ising model within the scaling region by integrating the interface energy over inverse temperature $β$, employing boundary-flip and cluster Monte Carlo methods to handle the log-ratio nature of the interface free energy. Using cross sections up to $96\times96$ and multiple boundary conditions, the authors extract the interface tension $σ$, its critical amplitude $σ_0$, and the universal ratio $R_{-}$, validating capillary-wave and semiclassical predictions and demonstrating no large logarithmic corrections. The main results are $σ_0 = 1.55(5)$ and $R_{-} = 0.1040(8)$, with consistent $σ$ across various finite-size fits and excellent agreement with theoretical expectations. The study advances numerical benchmarks for interface phenomena in the 3D Ising universality class and provides precise inputs for universal amplitude analyses in critical phenomena.

Abstract

Using the Monte Carlo method, we determine the free energy of the interface of the 3D Ising model in the scaling region. By integrating the interface energies over the inverse temperature $β$, we obtain estimates for the free energies of interfaces with cross sections up to 96 by 96, and for a range $0.223 \leq β\leq 0.23$. Our data yield a precise estimation of the interface tensions $σ$. We determine the amplitude $σ_0$ in the critical law $σ\sim σ_0 t^μ$ and estimate the combination $σξ^2$ which yields the universal constant $R_{-}$ in the critical limit.