A simple protocol for the probability weights of the simulated tempering algorithm: applications to first-order phase transitions

TL;DR

This paper introduces a simplified method to compute probability weights for simulated tempering using the transfer matrix's largest eigenvalue, enhancing efficiency in sampling systems with challenging phase spaces, especially during first-order phase transitions.

Contribution

The authors propose a straightforward approach to determine simulated tempering weights from the transfer matrix eigenvalue, reducing computational complexity and facilitating studies of first-order phase transitions.

Findings

Accurate weight estimation from transfer matrix eigenvalues.

Successful application to Ising, Blume-Capel, Blume-Emery-Griffiths, and Bell-Lavis models.

Effective sampling of systems with large free-energy barriers.

Abstract

The simulated tempering (ST) is an important method to deal with systems whose phase spaces are hard to sample ergodically. However, it uses accepting probabilities weights which often demand involving and time consuming calculations. Here it is shown that such weights are quite accurately obtained from the largest eigenvalue of the transfer matrix -- a quantity straightforward to compute from direct Monte Carlo simulations -- thus simplifying the algorithm implementation. As tests, different systems are considered, namely, Ising, Blume-Capel, Blume-Emery-Griffiths and Bell-Lavis liquid water models. In particular, we address first-order phase transition at low temperatures, a regime notoriously difficulty to simulate because the large free-energy barriers. The good results found (when compared with other well established approaches) suggest that the ST can be a valuable tool to address strong first-order phase transitions, a possibility still not well explored in the literature.