Comparing parallel- and simulated-tempering-enhanced sampling algorithms at phase-transition regimes

A single-walker approach for studying quasi-nonergodic systems

The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-nonergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for large parallel processing systems. The updated algorithm is tested on the Ising model and applied to the lattice-gas model for sorption in aerogel at low temperatures, when dynamics of the system is critically slowed down. It is demonstrated that the updated jump-walking simulations are able to produce equilibrium isotherms which are typically hidden by the hysteresis effect characteristic of the standard single-flip simulations.

On the use of mass scaling for stable and efficient simulated tempering with molecular dynamics

Simulated tempering (ST) is a generalized-ensemble algorithm that employs trajectories exploring a range of temperatures to effectively sample rugged energy landscapes. When implemented using the molecular dynamics method, ST can require the use of short time steps for ensuring the stability of trajectories at high temperatures. To address this shortcoming, a mass-scaling ST (MSST) method is presented in which the particle mass is scaled in proportion to the temperature. Mass scaling in the MSST method leads to velocity distributions that are independent of temperature and eliminates the need for velocity scaling after the accepted temperature updates that are required in conventional ST simulations. The homogeneity in time scales with changing temperature improves the stability of simulations and allows for the use of longer time steps at high temperatures. As a result, the MSST is found to be more efficient than the standard ST method, particularly for cases in which a large temperature range is employed. © 2016 Wiley Periodicals, Inc.

General approach for studying first-order phase transitions at low temperatures

By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small T's, it is possible to derive a generic analytic expression for appropriate order parameters, whose coefficients are obtained from simple simulations. Once in such regimes simulations by standard algorithms are not reliable; an enhanced tempering method, the parallel tempering-accurate for small and intermediate system sizes with rather low computational cost-is used. Finally, from finite size analysis, one can obtain the thermodynamic limit. The procedure is illustrated for four distinct models, demonstrating its power, e.g., to locate coexistence lines and the phase density at the coexistence.

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

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.