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We introduce a new update scheme to systematically improve the efficiency ofparallel tempering simulations. We show that by adapting the number of sweepsbetween replica exchanges to the canonical autocorrelation time, the averageround-trip time of a replica in temperature space can be significantlydecreased. The temperatures are not dynamically adjusted as in previousattempts but chosen to yield a 50% exchange rate of adjacent replicas. Weillustrate the new algorithm with results for the Ising model in two and theEdwards-Anderson Ising spin glass in three dimensions

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