Monte Carlo simulation of ice models

TL;DR

This paper introduces new Monte Carlo algorithms for simulating ice models, notably a cluster algorithm with near-zero dynamic exponent, enabling efficient critical phenomena analysis.

Contribution

The paper presents novel Monte Carlo algorithms, including a highly efficient cluster algorithm for the three-color ice model, improving simulation of critical ice models.

Findings

Cluster algorithm exhibits near-zero dynamic exponent.

Extensive simulations determine critical exponents for square ice and F models.

Algorithms outperform previous methods in efficiency for critical ice model simulations.

Abstract

We propose a number of Monte Carlo algorithms for the simulation of ice models and compare their efficiency. One of them, a cluster algorithm for the equivalent three colour model, appears to have a dynamic exponent close to zero, making it particularly useful for simulations of critical ice models. We have performed extensive simulations using our algorithms to determine a number of critical exponents for the square ice and F models.