Domain wall fluctuations of the six-vertex model at the ice point

TL;DR

This paper uses Monte-Carlo simulations to analyze the fluctuations of domain walls in the six-vertex model at the ice point, confirming Tracy-Widom distribution behavior and computing scaling coefficients.

Contribution

It provides high-precision analysis of domain wall fluctuations at the ice point, including confirmation of Tracy-Widom distribution and calculation of non-universal scaling coefficients.

Findings

Line fluctuations are of order N^{1/3}

Fluctuations follow Tracy-Widom distribution

Scaling coefficients are computed for various interaction strengths

Abstract

We report on Monte-Carlo simulations of the six-vertex model with domain wall boundary conditions. In thermal equilibrium such boundary conditions force a fluctuating line separating the disordered region from the perfectly ordered ones. Specifically we study the ice point at which all vertex weights are equal. With high precision the one-point fluctuations of the line are confirmed to be of order $N^{1/3}$ and governed by the Tracy-Widom distribution. Furthermore, the non-universal scaling coefficients are computed for a wide range of interaction strengths. A draft of this paper was completed in January 2019. We improved the presentation and updated references.