Rejection-free Monte Carlo Algorithms for Models with Continuous Degrees of Freedom

TL;DR

This paper introduces a rejection-free Monte Carlo algorithm for systems with continuous degrees of freedom, demonstrating its efficiency and accuracy on the 3D Heisenberg model, especially at low temperatures.

Contribution

The authors develop a general rejection-free Monte Carlo method applicable to continuous systems, improving computational efficiency over traditional Metropolis algorithms.

Findings

The algorithm accurately reproduces metastable state lifetimes.

It requires significantly less computational time at low temperatures.

Results agree with standard Metropolis dynamics.

Abstract

We construct a rejection-free Monte Carlo algorithm for a system with continuous degrees of freedom. We illustrate the algorithm by applying it to the classical three-dimensional Heisenberg model with canonical Metropolis dynamics. We obtain the lifetime of the metastable state following a reversal of the external magnetic field. Our rejection-free algorithm obtains results in agreement with a direct implementation of the Metropolis dynamic and requires orders of magnitude less computational time at low temperatures. The treatment is general and can be extended to other dynamics and other systems with continuous degrees of freedom.