Finite-Size Effects in the Interface of 3D Ising Model

TL;DR

This paper investigates finite-size effects at the interface of the 3D Ising model near criticality, demonstrating shape-dependent corrections that align with a capillary wave Gaussian model through numerical simulations.

Contribution

It provides the first detailed verification of shape-dependent finite-size corrections in the 3D Ising model interface using numerical simulations, supporting a long-standing conjecture.

Findings

Finite-size corrections depend strongly on lattice shape.

Numerical simulations confirm the Gaussian capillary wave model.

Supports conjecture on finite-size effects in Lattice Gauge Theories.

Abstract

The interface between domains of opposite magnetization in the 3D Ising model near the critical temperature displays universal finite-size effects which can be described in terms of a gaussian model of capillary waves. It turns out that these finite-size corrections depend rather strongly on the shape of the lattice. This prediction, which has no adjustable parameters, is tested and accurately verified for various lattice shapes by means of numerical simulations with a cluster algorithm. This supports also a long-standing conjecture on the finite-size effects in Wilson loops of Lattice Gauge Theories.