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

Abstract

Two important enhanced sampling algorithms, simulated (ST) and parallel (PT) tempering, are commonly used when ergodic simulations may be hard to achieve, e.g, due to a phase space separated by large free-energy barriers. This is so for systems around first-order phase transitions, a case still not fully explored with such approaches in the literature. In this contribution we make a comparative study between the PT and ST for the Ising (a lattice-gas in the fluid language) and the BEG (a lattice-gas with vacancies) models at phase transition regimes. We show that although the two methods are equivalent in the limit of sufficiently long simulations, the PT is more advantageous than the ST with respect to all the analysis performed: convergence towards the stationarity; frequency of tunneling between phases at the coexistence; and decay of time-displaced correlation functions of thermodynamic quantities. Qualitative arguments for why one may expect better results from the PT than the ST near phase transitions conditions are also presented.

References in corpus (20)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Simulated Tempering: A New Monte Carlo Scheme
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Parallel Tempering Algorithm for Conformational Studies of Biological Molecules
• Feedback-optimized parallel tempering Monte Carlo
• Optimized parallel tempering simulations of proteins
• Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model
• First order phase transition in the Quantum Adiabatic Algorithm
• Multibondic Cluster Algorithm for Monte Carlo Simulations of First-Order Phase Transitions
• The incomplete beta function law for parallel tempering sampling of classical canonical systems
• Make life simple: unleash the full power of the parallel tempering algorithm
• Generalized Ensemble Simulations for Complex Systems
• Simulation via Direct Computation of Partition Functions
• The Approach to Ergodicity in Monte Carlo Simulations
• Optimizing Replica Exchange Moves For Molecular Dynamics
• Statistical Mechanics of Time Independent Non-Dissipative Nonequilibrium States
• First-order phase transitions: A study through the parallel tempering method
• Obtaining pressure versus concentration phase diagrams in spin systems from Monte Carlo simulations
• Boundary field induced first-order transition in the 2D Ising model: numerical study

Cited by in corpus (7)

• General approach for studying first-order phase transitions at low temperatures
• Exploiting a semi-analytic approach to study first order phase transitions
• Comparing different protocols of temperature selection in the parallel tempering method
• A simple protocol for the probability weights of the simulated tempering algorithm: applications to first-order phase transitions
• Determining efficient temperature sets for the simulated tempering method
• Efficient simulated tempering with approximated weights: Applications to first-order phase transitions
• A single-walker approach for studying quasi-ergodic systems