The bounded 15-vertex model

TL;DR

This paper investigates the 15-vertex model in statistical mechanics on a square domain with various boundary conditions, revealing complex equilibrium states and limit shapes through simulation.

Contribution

It introduces a dynamic version of the 15-vertex model and explores its equilibrium states under diverse boundary configurations, extending understanding beyond the six-vertex model.

Findings

Almost isotropic non-trivial limit shapes observed

Dynamic simulation reveals complex equilibrium states

Boundary conditions significantly influence limit shapes

Abstract

The 15-vertex model of Statistical Mechanics is studied on a square domain with partially oriented boundary. With DWBC the model would reduce to the six-vertex model, but more general boundary configurations are available. After establishing the dynamic version of the model we simulate with it to find the typical equilibrium states for a set of increasingly complex boundaries. Among others they yield almost isotropic non-trivial limit shapes even though the microscopic model is highly asymmetric.