Cluster Hybrid Monte Carlo Simulation Algorithms

TL;DR

This paper demonstrates that hybrid Monte Carlo algorithms combining Metropolis and Wolff cluster flips significantly improve simulation efficiency and accuracy for spin models, especially in complex systems like spin-3/2 Ising.

Contribution

It introduces hybrid algorithms that combine Metropolis and Wolff cluster flips, enhancing performance and reducing errors in spin system simulations.

Findings

Hybrid algorithms outperform pure methods in efficiency.

Adding cluster flips reduces statistical errors.

Hybridization mitigates systematic errors from random number generators.

Abstract

We show that addition of Metropolis single spin-flips to the Wolff cluster flipping Monte Carlo procedure leads to a dramatic {\bf increase} in performance for the spin-1/2 Ising model. We also show that adding Wolff cluster flipping to the Metropolis or heat bath algorithms in systems where just cluster flipping is not immediately obvious (such as the spin-3/2 Ising model) can substantially {\bf reduce} the statistical errors of the simulations. A further advantage of these methods is that systematic errors introduced by the use of imperfect random number generation may be largely healed by hybridizing single spin-flips with cluster flipping.