Universal behaviour of interfaces in 2d and dimensional reduction of Nambu-Goto strings

TL;DR

This paper introduces a universal effective model for 2d interfaces, derived from Nambu-Goto strings, which accurately predicts interface free energy and aligns with exact results in the 2d Ising model.

Contribution

It presents a simple, universal effective model for 2d interfaces that emerges from a dimensional reduction of the Nambu-Goto string framework.

Findings

Model's predictions match exact 2d Ising results

Universal behavior of interfaces in 2d models

Dimensional reduction links string theory to statistical interfaces

Abstract

We propose a simple effective model for the description of interfaces in 2d statistical models, based on the first-order treatment of an action corresponding to the length of the interface. The universal prediction of this model for the interface free energy agrees with the result of an exact calculation in the case of the 2d Ising model. This model appears as a dimensional reduction of the Nambu-Goto stringy description of interfaces in 3d, i.e., of the capillary wave model.