  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.
