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In replica exchange Monte Carlo (REM), tuning of the temperature set and theexchange scheduling are crucial in improving the accuracy and reducingcalculation time. In multi-dimensional simulated tempering, the first orderphase transition is accessible. Therefore it is important to study the tuningof parameter set and the scheduling of exchanges in the parallel counterpart,the multi-dimensional REM. We extend Hukushima's constant exchange probabilitymethod to multi-dimensional REM for the parameter set. We further propose acombined method to use this set and the Bittner-Nussbaumer-Janke's PT taualgorithm for scheduling. We test the proposed method in two-dimensional spin-1Blume-Capel model and find that it works efficiently, including the vicinity ofthe first order phase transition.

journal of statistical mechanics

Extension of the constant exchange probability method to  multi-dimensional replica exchange Monte Carlo applied to the tri-critical  spin-1 Blume-Capel model