A comparative study of selected parallel tempering methods

TL;DR

This paper compares various parallel tempering methods, analyzing their accuracy and efficiency across different models, and identifies key factors and algorithms that improve performance in sampling complex systems.

Contribution

It provides a comprehensive comparison of parallel tempering schemes, including novel exchange methods, and evaluates their effectiveness on 2D and 3D spin models.

Findings

Cluster algorithms significantly improve efficiency.

Using local moves related to correlation times enhances sampling.

Nearest-neighbor approaches are most effective for 3D spin glasses.

Abstract

We review several parallel tempering schemes and examine their main ingredients for accuracy and efficiency. The present study covers two selection methods of temperatures and several choices for the exchange of replicas, including a recent novel all-pair exchange method. We compare the resulting schemes and measure specific heat errors and efficiency using the two-dimensional (2D) Ising model. Our tests suggest that, an earlier proposal for using numbers of local moves related to the canonical correlation times is one of the key ingredients for increasing efficiency, and protocols using cluster algorithms are found to be very effective. Some of the protocols are also tested for efficiency and ground state production in 3D spin glass models where we find that, a simple nearest-neighbor approach using a local n-fold way algorithm is the most effective. Finally, we present evidence that the asymptotic limits of the ground state energy for the isotropic case and that of an anisotropic case of the 3D spin-glass model are very close and may even coincide.