Parallelization of Markov chain generation and its application to the multicanonical method

TL;DR

This paper introduces a straightforward parallelization algorithm for Markov chain generation, enabling efficient multicanonical calculations in statistical physics models like the 2D Ising model.

Contribution

It presents a novel parallelization method for Markov chains that maintains detailed balance, applied successfully to multicanonical simulations.

Findings

Accurate estimation of multicanonical weights achieved

Parallel Markov chains effectively combined without loss of detailed balance

Demonstrated applicability to 2D Ising model simulations

Abstract

We develop a simple algorithm to parallelize generation processes of Markov chains. In this algorithm, multiple Markov chains are generated in parallel and jointed together to make a longer Markov chain. The joints between the constituent Markov chains are processed using the detailed balance. We apply the parallelization algorithm to multicanonical calculations of the two-dimensional Ising model and demonstrate accurate estimation of multicanonical weights.