Monte Carlo methods beyond detailed balance

• We propose a Monte Carlo approach, which is not restricted by detailed balance.
• The high efficiency of this new approach is demonstrated in a simple model.
• Its general applicability is demonstrated by applying it to the Ising model.

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.