Extension of the constant exchange probability method to multi-dimensional replica exchange Monte Carlo applied to the tri-critical spin-1 Blume-Capel model

TL;DR

This paper extends the constant exchange probability method to multi-dimensional replica exchange Monte Carlo, improving efficiency in studying phase transitions in the spin-1 Blume-Capel model.

Contribution

It introduces a novel extension of the constant exchange probability method for multi-dimensional REM and combines it with a scheduling algorithm for better performance.

Findings

Efficient sampling near first order phase transitions.

Successful application to the two-dimensional spin-1 Blume-Capel model.

Enhanced accuracy and reduced computation time.

Abstract

In replica exchange Monte Carlo (REM), tuning of the temperature set and the exchange scheduling are crucial in improving the accuracy and reducing calculation time. In multi-dimensional simulated tempering, the first order phase transition is accessible. Therefore it is important to study the tuning of parameter set and the scheduling of exchanges in the parallel counterpart, the multi-dimensional REM. We extend Hukushima's constant exchange probability method to multi-dimensional REM for the parameter set. We further propose a combined method to use this set and the Bittner-Nussbaumer-Janke's PT tau algorithm for scheduling. We test the proposed method in two-dimensional spin-1 Blume-Capel model and find that it works efficiently, including the vicinity of the first order phase transition.