The partition function of interfaces from the Nambu-Goto effective string theory

TL;DR

This paper derives an exact partition function for interfaces modeled by the Nambu-Goto string, matching Monte Carlo data in the 3D Ising model and advancing the theoretical understanding of interface physics.

Contribution

It provides a novel exact expression for the interface partition function using covariant quantization, resumming the loop expansion and aligning with numerical data.

Findings

Exact partition function matches Monte Carlo data for large interfaces.

Resums loop expansion of Nambu-Goto model in physical gauge.

Agreement with previous analyses of Ising model observables.

Abstract

We consider the Nambu-Goto bosonic string model as a description of the physics of interfaces. By using the standard covariant quantization of the bosonic string, we derive an exact expression for the partition function in dependence of the geometry of the interface. Our expression, obtained by operatorial methods, resums the loop expansion of the NG model in the "physical gauge" computed perturbatively by functional integral methods in the literature. Recently, very accurate Monte Carlo data for the interface free energy in the 3d Ising model became avaliable. Our proposed expression compares very well to the data for values of the area sufficiently large in terms of the inverse string tension. This pattern is expected on theoretical grounds and agrees with previous analyses of other observables in the Ising model.