Condensation of handles in the interface of 3D Ising model

TL;DR

This paper investigates the complex topological structure of domain interfaces in the 3D Ising model near criticality, revealing fractal behavior, a linear relationship between area and genus, and finite-size effects on entropy.

Contribution

It provides a detailed analysis of the topological and fractal properties of interfaces in the 3D Ising model, highlighting the relationship between area and genus and finite-size effects.

Findings

Interface exhibits fractal behavior with high handle density

Mean area is nearly linear with genus

Finite-size effects influence entropy exponent

Abstract

We analyze the microscopic, topological structure of the interface between domains of opposite magnetization in 3D Ising model near the critical point. This interface exhibits a fractal behaviour with a high density of handles. The mean area is an almost linear function of the genus. The entropy exponent is affected by strong finite-size effects.