Abstract
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.
Similar content being viewed by others
References
Okamoto, Y.: J. Mol. Graph. Model. 22, 425 (2004)
Nadler, W., Hansmann, U.H.E.: Phys. Rev. E 75, 026109 (2007)
Swendsen, R.H., Wang, J.-S.: Phys. Rev. Lett. 57, 2607 (1986)
Geyer, C.: In: Keramidas, E.M. (ed.) Computing Science and Statistics: 23rd Symposium on the Interface, p. 156. Interface Foundation, Fairfax Station (1991)
Hukushima, K., Nemoto, K.: J. Phys. Soc. Jpn. 65, 1604 (1996)
Earl, D.J., Deem, M.W.: Phys. Chem. Chem. Phys. 7, 3910 (2005)
Katzgraber, H.G., Körner, M., Young, A.P.: Phys. Rev. B 73, 224432 (2006)
Banos, R.A., Cruz, A., Fernandez, L.A., Gil-Narvion, J.M., Gordillo-Guerrero, A., Guidetti, M., Maiorano, A., Mantovani, F., Marinari, E., Martin-Mayor, V., et al.: J. Stat. Mech. Theory Exp. 2010, P06026 (2010)
Hansmann, U.H.E.: Chem. Phys. Lett. 281, 140 (1997)
Schug, A., Herges, T., Verma, A., Wenzel, W.: J. Phys., Condens. Matter 17, S1641 (2005)
Burgio, G., Fuhrmann, M., Kerler, W., Muller-Preussker, M.: Phys. Rev. D 75, 014504 (2007)
Hukushima, K., Iba, Y.: In: Gubernatis, J.E. (ed.) The Monte Carlo Method in the Physical Sciences: Celebrating the 50th Anniversary of the Metropolis Algorithm. AIP Conf. Proc., vol. 690, pp. 200–206. AIP, New York (2003)
Machta, J.: Phys. Rev. E 82, 026704 (2010)
Machta, J.: Phys. Rev. E 80, 056706 (2009)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Science 220, 671 (1983)
van Laarhoven, P., Aarts, E.: Simulated Annealing: Theory and Applications. Reidel, Dordrecht (1987)
Anderson, J.B.: J. Chem. Phys. 63, 1499 (1975)
Grassberger, P.: Comput. Phys. Commun. 147, 64 (2002)
Doucet, A., de Freitas, N., Gordon, N. (eds.): Sequential Monte Carlo Methods in Practice. Springer, New York (2001)
Katzgraber, H.G., Trebst, S., Huse, D.A., Troyer, M.: J. Stat. Mech. 03018 (2006)
Trebst, S., Troyer, M., Hansmann, U.H.E.: J. Chem. Phys. 124, 174903 (2006)
Bittner, E., Nußbaumer, A., Janke, W.: Phys. Rev. Lett. 101, 130603 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Machta, J., Ellis, R.S. Monte Carlo Methods for Rough Free Energy Landscapes: Population Annealing and Parallel Tempering. J Stat Phys 144, 541–553 (2011). https://doi.org/10.1007/s10955-011-0249-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-011-0249-0