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## Parallel tempering
## Additional recommended knowledgeTypically a MC simulation using a Metropolis-Hastings update consists of a single stochastic process that evaluates the energy of the system and accepts/rejects updates based on the temperature If we were to run two simulations at temperatures separated by a Δ Another way to interpret this overlap is to say that system configurations sampled at temperature This update can be generalized to more than two systems. By a careful choice of temperatures and number of systems one can achieve an improvement in the mixing properties of a set of Monte Carlo simulations that exceeds the extra computational cost of running parallel simulations. Other considerations to be made: increasing the number of different temperatures can have a detrimental effect, as one can think of the 'lateral' movement of a given system across temperatures as a diffusion process. Set up is important as there must be a practical histogram overlap to achieve a reasonable probability of lateral moves. The parallel tempering method can be used as a super simulated annealing that does not need restart, since a system at high temperature can feed new local optimizers to a system at low temperature, allowing tunneling between metastable states and improving convergence to a global optimum. ## References**^**C. J. Geyer, in Computing Science and Statistics Proceedings of the 23rd Symposium on the Interface, American Statistical Association, New York, 1991, p. 156.
Parallel tempering: Theory, applications, and new perspectives, David J. Earl and Michael W. Deem, Phys. Chem. Chem. Phys., 2005, 7, 3910 |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Parallel_tempering". A list of authors is available in Wikipedia. |