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Parallel tempering, in physics and statistics, is a computer simulation method typically used to find the lowest energy state of a system of many interacting particles. It addresses the problem that at high temperatures, one may have a stable state different from low temperature, whereas simulations at low temperatures may become "stuck" in a metastable state. It does this by using the fact that the high temperature simulation may visit states typical of both stable and metastable low temperature states.
More specifically, parallel tempering (also known as replica exchange MCMC sampling), is a simulation method aimed at improving the dynamic properties of Monte Carlo method simulations of physical systems, and of Markov chain Monte Carlo (MCMC) sampling methods more generally. The replica exchange method was originally devised by Robert Swendsen and J. S. Wang,[1] then extended by Charles J. Geyer,[2] and later developed further by Giorgio Parisi,[3]
Koji Hukushima and Koji Nemoto,[4]
and others.[5][6]
Y. Sugita and Y. Okamoto also formulated a molecular dynamics version of parallel tempering; this is usually known as replica-exchange molecular dynamics or REMD.[7]
Essentially, one runs N copies of the system, randomly initialized, at different temperatures. Then, based on the Metropolis criterion one exchanges configurations at different temperatures. The idea of this method
is to make configurations at high temperatures available to the simulations at low temperatures and vice versa.
This results in a very robust ensemble which is able to sample both low and high energy configurations.
In this way, thermodynamical properties such as the specific heat, which is in general not well computed in the canonical ensemble, can be computed with great precision.
^Swendsen RH and Wang JS (1986) Replica Monte Carlo simulation of spin glasses Physical Review Letters 57 : 2607–2609
^C. J. Geyer, (1991) in Computing Science and Statistics, Proceedings of the 23rd Symposium on the Interface, American Statistical Association, New York, p. 156.
^Marinari, E; Parisi, G (1992-07-15). "Simulated Tempering: A New Monte Carlo Scheme". Europhysics Letters (EPL). 19 (6): 451–458. arXiv:hep-lat/9205018. Bibcode:1992EL.....19..451M. doi:10.1209/0295-5075/19/6/002. ISSN 0295-5075. S2CID 250781561.
^Hukushima, Koji & Nemoto, Koji (1996). "Exchange Monte Carlo method and application to spin glass simulations". J. Phys. Soc. Jpn. 65 (6): 1604–1608. arXiv:cond-mat/9512035. Bibcode:1996JPSJ...65.1604H. doi:10.1143/JPSJ.65.1604. S2CID 15032087.
^Marco Falcioni & Michael W. Deem (1999). "A Biased Monte Carlo Scheme for Zeolite Structure Solution". J. Chem. Phys. 110 (3): 1754. arXiv:cond-mat/9809085. Bibcode:1999JChPh.110.1754F. doi:10.1063/1.477812. S2CID 13963102.
^David J. Earl and Michael W. Deem (2005) "Parallel tempering: Theory, applications, and new perspectives", Phys. Chem. Chem. Phys., 7, 3910
^Y. Sugita & Y. Okamoto (1999). "Replica-exchange molecular dynamics method for protein folding". Chemical Physics Letters. 314 (1–2): 141–151. Bibcode:1999CPL...314..141S. doi:10.1016/S0009-2614(99)01123-9.
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