Monte Carlo with Absorbing Markov Chains: Fast Local Algorithms for Slow Dynamics

TL;DR

The paper introduces a class of Monte Carlo algorithms using absorbing Markov chains that significantly accelerate simulations of slow dynamics, such as metastable escape in Ising models, outperforming traditional methods.

Contribution

It presents a new family of Monte Carlo algorithms incorporating absorbing Markov chains, generalizing the $n$-fold way, with demonstrated efficiency improvements.

Findings

Algorithms accurately model metastable escape in Ising models.

Higher-order algorithms are many times faster than traditional methods.

Good agreement with theoretical predictions observed.

Abstract

A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape from the metastable state in the two-dimensional square-lattice nearest-neighbor Ising ferromagnet in an unfavorable applied field, and the agreement with theoretical predictions is very good. It is demonstrated that the higher-order algorithms can be many orders of magnitude faster than either the traditional Monte Carlo or $n$-fold way algorithms.