Monte Carlo methods beyond detailed balance

Abstract

Monte Carlo algorithms are nearly always based on the concept of detailed balance and ergodicity. In this paper we focus on algorithms that do not satisfy detailed balance. We introduce a general method for designing non-detailed balance algorithms, starting from a conventional algorithm satisfying detailed balance. This approach is first applied to a very simple model, which shows the basic viability of the method. Then we apply it to the Ising model, where we find that the method is an improvement compared to the standard Metropolis algorithm, be it with a modest gain of a factor 2.3. (C) 2014 Elsevier B.V. All rights reserved.