The genus-zero five-vertex model

TL;DR

This paper analyzes the five-vertex model with genus-zero weights, deriving its phase diagram, free energy, and limit shapes, and reveals that its surface tension has a trivial potential, allowing explicit shape parameterizations.

Contribution

It provides the first exact analysis of the phase diagram, free energy, and limit shapes for the genus-zero five-vertex model, with explicit parameterizations.

Findings

Derived the exact phase diagram for the model.

Calculated the free energy and surface tension explicitly.

Provided explicit parameterizations of the limit shapes.

Abstract

We study the free energy and limit shape problem for the five-vertex model with periodic "genus zero" weights. We derive the exact phase diagram, free energy and surface tension for this model. We show that its surface tension has trivial potential and use this to give explicit parameterizations of limit shapes.