Six vertex model with domain-wall boundary conditions in the Bethe-Peierls approximation

TL;DR

This paper applies the Bethe-Peierls approximation combined with belief propagation to analyze arctic curves in the six vertex model, providing accurate estimates of phase boundaries with minimal computational effort.

Contribution

It demonstrates that the Bethe-Peierls method yields close approximations to exact results for the six vertex model with boundary conditions, even where exact solutions are unknown.

Findings

Approximate arctic curves closely match known exact results.

Method effectively estimates phase boundaries in complex boundary conditions.

Simplifies analysis of the six vertex model with minimal computational resources.

Abstract

We use the Bethe-Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice with partial domain-wall boundary conditions. We show that this rather simple approximation yields results that are remarkably close to the exact ones when these are known, and allows one to estimate the location of the phase boundaries with relative little effort in cases in which exact results are not available.