Fluid Interfaces in the 3D Ising Model as a Dilute Gas of Handles

TL;DR

This paper models fluid interfaces in the 3D Ising model's rough phase as dilute gases of microscopic handles, revealing how topology affects interface stiffness and width scaling.

Contribution

It introduces a novel topological description of interfaces as dilute handle gases and quantifies how topology influences interface properties.

Findings

Interfaces are described as dilute gases of handles.

Interface stiffness increases with genus.

Width scales logarithmically with lattice size.

Abstract

We study the topology of fluid interfaces in the 3D Ising model in the rough phase. It turns out that such interfaces are accurately described as dilute gases of microscopic handles, and the stiffness of the interface increases with the genus. The number of configurations of genus $g$ follows a Poisson-like distribution. The probability per unit area for creating a handle is well fitted in a wide range of the inverse temperature $\beta$ near the roughening point by an exponentially decreasing function of $\beta$. The procedure of summing over all topologies results in an effective interface whose squared width scales logarithmically with the lattice size.