Feedback-optimized parallel tempering Monte Carlo

Abstract

We introduce an algorithm for systematically improving the efficiency of paralleltempering Monte Carlo simulations by optimizing the simulated temperature set. Ourapproach is closely related to a recently introduced adaptive algorithm that optimizesthe simulated statistical ensemble in generalized broad-histogram Monte Carlosimulations. Conventionally, a temperature set is chosen in such a way that theacceptance rates for replica swaps between adjacent temperatures are independent ofthe temperature and large enough to ensure frequent swaps. In this paper, weshow that by choosing the temperatures with a modified version of the optimizedensemble feedback method we can minimize the round-trip times between the lowestand highest temperatures which effectively increases the efficiency of the paralleltempering algorithm. In particular, the density of temperatures in the optimizedtemperature set increases at the ‘bottlenecks’ of the simulation, such as phasetransitions. In turn, the acceptance rates are now temperature dependent in theoptimized temperature ensemble. We illustrate the feedback-optimized paralleltempering algorithm by studying the two-dimensional Ising ferromagnet and thetwo-dimensional fully frustrated Ising model, and briefly discuss possible feedbackschemes for systems that require configurational averages, such as spin glasses.