Designed-walk replica-exchange method for simulations of complex systems

TL;DR

This paper introduces a novel replica-exchange method where replicas follow a predetermined temperature route, enhancing tunneling efficiency and maintaining detailed balance, demonstrated on a 2D Ising model.

Contribution

The paper presents a new planned-route implementation of REM that improves tunneling frequency and maintains detailed balance, differing from traditional random-walk approaches.

Findings

Reproduces results of conventional REM on a 2D Ising model.

Increases tunneling counts by over three times compared to random-walk REM.

Ensures almost constant tunneling period between highest and lowest temperatures.

Abstract

We propose a new implementation of the replica-exchange method (REM) in which replicas follow a pre-planned route in temperature space instead of a random walk. Our method satisfies the detailed balance condition in the proposed route. The method forces tunneling events between the highest and lowest temperatures to happen with an almost constant period. The number of tunneling counts is proportional to that of the random-walk REM multiplied by the square root of moving distance in temperature space. We applied this new implementation to two kinds of REM and compared the results with those of the conventional random-walk REM. The test system was a two-dimensional Ising model, and our new method reproduced the results of the conventional random-walk REM and improved the tunneling counts by three times or more than that of the random-walk REM.