Effective string theory description of the interface free energy

TL;DR

This paper compares the Nambu-Goto effective string model predictions with high-precision Monte Carlo results for 3D Ising model interfaces, deriving the spectrum and analyzing corrections near the deconfinement transition.

Contribution

It provides a detailed comparison of the effective string model with numerical data, including spectrum derivation and correction analysis, enhancing understanding of interface free energy in the 3D Ising model.

Findings

Perturbative expansion matches previous gauge results.

Derived the effective string spectrum with boundary condition effects.

Estimated key amplitude ratios and analyzed near-deconfinement behavior.

Abstract

We compare the predictions of the Nambu-Goto effective string model with a set of high precision Monte Carlo results for interfaces with periodic boundary conditions in the 3D Ising model. We compute the free energy in the covariant gauge exactly, up to the inclusion of the Liouville mode. The perturbative expansion of this result agrees both with the result evaluated several years ago by Dietz and Filk in the physical gauge and with a recent calculation with the Polchinski-Strominger action. We also derive the effective string spectrum which, because of the different boundary conditions, is very different from the well known one of Arvis. Taking into proper account the effective string corrections and exploiting some technical improvements in the simulations we obtain precise estimate of the amplitude ratios T_c/\sqrt{sigma}, m_{0++}/\sqrt{\sigma} and sigma xi_{2nd}^2. We also discuss the behaviour of the effective string free energy in the dimensional reduction limit (i.e., near the deconfinement transition of the dual 3d gauge Ising model) and its relationship with the 2d Ising model interfaces