Comparing different protocols of temperature selection in the parallel tempering method

TL;DR

This paper compares various temperature selection protocols in parallel tempering Monte Carlo simulations, highlighting the effectiveness of the constant entropy method (CEM) for systems with complex free-energy landscapes.

Contribution

The study introduces a practical approach to determine entropy without numerical integration, and evaluates CEM against other schemes across different phase transition types.

Findings

CEM improves sampling efficiency in rugged landscapes.

CEM is effective for both first- and second-order phase transitions.

The proposed entropy determination method simplifies temperature selection.

Abstract

Parallel tempering Monte Carlo simulations have been applied to a variety of systems presenting rugged free-energy landscapes. Despite this, its efficiency depends strongly on the temperature set. With this query in mind, we present a comparative study among different temperature selection schemes in three lattice-gas models. We focus our attention in the constant entropy method (CEM), proposed by Sabo {\it et al}. In the CEM, the temperature is chosen by the fixed difference of entropy between adjacent replicas. We consider a method to determine the entropy which avoids numerical integrations of the specific heat and other thermodynamic quantities. Different analyses for first- and second-order phase transitions have been undertaken, revealing that the CEM may be an useful criterion for selecting the temperatures in the parallel tempering