Tune the autocorrelation time and unleash the full power of the parallel tempering algorithm ∗

We introduce a new update scheme to systematically improve the efficiency of parallel tempering Monte Carlo simulations by taking into account the temperature dependence of autocorrelation times. In contrast to previous attempts the temperatures are not dynamically adjusted but chosen in such a way that the acceptance rate for proposed exchanges of all adjacent replica is about 50%. We show that by adapting the number of sweeps between the parallel tempering moves to the canonical autocorrelation time, the average round-trip time of a replica between the lowest and the highest temperatures is significantly decreased and, therefore, the efficiency of the parallel tempering algorithm is considerably improved. We illustrate the new algorithm with results for the two-dimensional Ising model and propose a toy model to find the optimal parameter set for the parallel tempering routine within no time.