Accelerating Multicanonical Sampling with Irreversibility

TL;DR

This paper introduces an irreversibility technique to enhance multicanonical Monte Carlo simulations, significantly speeding up ground-state searches in complex physical systems by reducing convergence time and variance.

Contribution

The authors apply irreversibility via the lifting approach to multicanonical Monte Carlo, achieving substantial speedups and improved convergence in physical system simulations.

Findings

2-4 times speedup in 2D Ising model ground-state search

Up to tenfold speedup in Edwards-Anderson spin glass

Narrower distribution of round-trip times indicating faster convergence

Abstract

Flat-histogram Monte Carlo simulations are well-established, robust methods to perform random walks in a physical observable or parameter space, making them suitable for finding ground states or studying phase transitions in complex systems in statistical physics. However, their efficiency can be limited by the time to attain the desired flat distribution, which is generally unknown prior to the simulations. In particular, they might suffer from slowing down towards the end of a simulation due to the diffusive nature of random walks. In this work we apply irreversibility to the multicanonical Monte Carlo method via the lifting approach to alleviate this behavior. We achieve a 2-4 times speedup in ground-state search for a two-dimensional (2D) Ising model, and up to an order of magnitude of speedup for finding the ground-state energy in an Edwards-Anderson spin glass, compared to traditional multicanonical sampling. The round-trip times between ground states show a narrower distribution and are significantly shorter compared to the reversible counterpart, suggesting that a lower convergence time with a smaller time variance is feasible.