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 efficiency of the two methods are compared. For large systems, population annealing initially converges to equilibrium more rapidly than parallel tempering for the same amount of computational work. However, parallel tempering converges exponentially and population annealing inversely in the computational work so that ultimately parallel tempering approaches equilibrium more rapidly than population annealing.