Efficient simulated tempering with approximated weights: Applications to first-order phase transitions

摘要

Simulated tempering (ST) has attracted a great deal of attention in the lastyears, due to its capability to allow systems with complex dynamics to escapefrom regions separated by large entropic barriers. However its performance isstrongly dependent on basic ingredients, such as the choice of the set oftemperatures and their associated weights. Since the weight evaluations are nottrivial tasks, an alternative approximated approach was proposed by Park andPande (Phys. Rev. E {\bf 76}, 016703 (2007)) to circumvent this difficulty.Here we present a detailed study about this procedure by comparing itsperformance with exact (free-energy) weights and other methods, its dependenceon the total replica number $R$ and on the temperature set. The ideas above areanalyzed in four distinct lattice models presenting strong first-order phasetransitions, hence constituting ideal examples in which the performance ofalgorithm is fundamental. In all cases, our results reveal that approximatedweights work properly in the regime of larger $R$'s. On the other hand, forsufficiently small $R$ its performance is reduced and the systems do not crossproperly the free-energy barriers. Finally, for estimating reliable temperaturesets, we consider a simple protocol proposed at Comp. Phys. Comm. {\bf 128},2046 (2014).