Monte Carlo Methods for Rough Free Energy Landscapes: Population Annealing and Parallel Tempering

Parallel tempering and population annealing are both effective methods for simulating equilibrium systems with rough free energy landscapes. Parallel tempering, also known as replica exchange Monte Carlo, is a Markov chain Monte Carlo method while population annealing is a sequential Monte Carlo method. Both methods overcome the exponential slowing associated with high free energy barriers. The convergence properties and efficiencies of the two methods are compared. For large systems, population annealing is closer to equilibrium than parallel tempering for short simulations. However, with respect to the amount of computation, parallel tempering converges exponentially while population annealing converges only inversely. As a result, for sufficiently long simulations parallel tempering approaches equilibrium more quickly than population annealing.