Static properties of 2D spin-ice as a sixteen-vertex model

TL;DR

This paper investigates the static properties and phase diagram of 2D spin-ice models using Monte Carlo simulations, mean-field approximations, and cavity methods, providing insights relevant to artificial spin ice experiments.

Contribution

It introduces a comprehensive analysis combining simulations and mean-field theory for the sixteen-vertex model, enhancing understanding of 2D spin-ice properties.

Findings

Determined the phase diagram of the model.

Compared mean-field and finite-dimensional results.

Discussed implications for artificial spin ice experiments.

Abstract

We present a thorough study of the static properties of 2D models of spin-ice type on the square lattice or, in other words, the sixteen-vertex model. We use extensive Monte Carlo simulations to determine the phase diagram and critical properties of the finite dimensional system. We put forward a suitable mean-field approximation, by defining the model on carefully chosen trees. We employ the cavity (Bethe-Peierls) method to derive self-consistent equations, the fixed points of which yield the equilibrium properties of the model on the tree-like graph. We compare mean-field and finite dimensional results. We discuss our findings in the context of experiments in artificial two dimensional spin ice.