Measuring free energy in parallel tempering Monte Carlo

TL;DR

This paper presents an efficient method for measuring absolute free energy in parallel tempering Monte Carlo, demonstrating comparable accuracy to population annealing with fewer temperature points by longer simulation times.

Contribution

It introduces an exponential averaging approach for free energy measurement in parallel tempering and compares its effectiveness with population annealing using a spin glass model.

Findings

Parallel tempering can measure free energy efficiently with fewer temperatures.

Longer simulation times at each temperature improve measurement accuracy.

Parallel tempering's performance is comparable to population annealing in free energy estimation.

Abstract

An efficient approach of measuring the absolute free energy in parallel tempering Monte Carlo using the exponential averaging method is discussed and the results are compared with those of population annealing Monte Carlo using the three-dimensional Edwards-Anderson Ising spin glass model as benchmark tests. Numerical results show that parallel tempering, even though uses a much less number of temperatures than population annealing, can nevertheless equally efficiently measure the absolute free energy by simulating each temperature for longer times.