A constant entropy increase model for the selection of parallel tempering ensembles

Dubravko Sabo,Markus Meuwly,David L. Freeman,J. D. Doll

doi:10.1063/1.2907846

Abstract

The present paper explores a simple approach to the question of parallel tempering temperature selection. We argue that to optimize the performance of parallel tempering it is reasonable to require that the increase in entropy between successive temperatures be uniform over the entire ensemble. An estimate of the system's heat capacity, obtained either from experiment, a preliminary simulation, or a suitable physical model, thus provides a means for generating the desired tempering ensemble. Applications to the two-dimensional Ising problem indicate that the resulting method is effective, simple to implement, and robust with respect to its sensitivity to the quality of the underlying heat capacity model.

Highlights

Stochastic quadrature methods are valuable tools in the study of many-body systems
Parallel tempering methods provide a general and effective technique for dealing with sparse sampling issues.[3,4,5,6]. The essence of these procedures is to create an ensemble of replicas of the system of interest corresponding to a range of one or more control parameters and to utilize the resulting ensemble to improve the sampling
If the tempering control parameter involved is the system’s temperature, the strategy is to use information from the ensemble’s high-temperature members, where activation barriers are more surmounted, to improve the sampling at lower temperatures, where barrier crossings are otherwise exponentially suppressed. This is accomplished by introducing attempted exchanges of configurations between ensemble members. For these attempted moves to be useful, the temperature range of the ensemble must be sufficiently large that its higher energy members can surmount relevant activation barriers and the spacing must be sufficiently small that exchange attempts between the various temperatures are statistically significant

Summary

INTRODUCTION

Stochastic quadrature methods are valuable tools in the study of many-body systems They offer a general approach to broad classes of both classical[1] and quantum-mechanical problems.[2] A common practical issue associated with the application of these methods is coping with the “sparse” probability distributions that accompany activated or “rare-event” processes. If the tempering control parameter involved is the system’s temperature, the strategy is to use information from the ensemble’s high-temperature members, where activation barriers are more surmounted, to improve the sampling at lower temperatures, where barrier crossings are otherwise exponentially suppressed. This is accomplished by introducing attempted exchanges of configurations between ensemble members. III, we compare the performance of various temperature selection techniques when applied to a common problem

FORMAL DEVELOPMENTS

NUMERICAL EXAMPLE

Method

SUMMARY