Analyzing and validating simulated tempering implementations at phase transition regimes

Abstract

This work presents a comprehensive analysis of key elements determining the efficiency of Simulated Tempering implementations for lattice models. Important aspects like the proper choice of the replicas temperature set ϒR, their quantity R and adequate estimation of the weight factors (establishing the probabilities of jumps between the replicas) are considered. A number of tests to validate distinct ST implementations – as well as to characterize convergence and fluctuations (this latter, after reaching the steady condition) of the thermodynamic estimators – is proposed. Also, by combining the ST method with the so called fixed exchange frequency protocol (to determine ϒR), a new procedure to calculate critical temperatures is developed. As cases studies, two commonly addressed lattice models are discussed, the Blume–Emery–Griffiths and Bell–Lavis. Their detailed investigation at the coexistence condition or under first order phase transition regimes allows to properly inspect factors like, pace of convergence, tunneling between replicas and minimal values of the highest replica temperature TR, affecting a good overall performance of the ST method.