Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T16:28:09.395Z Has data issue: false hasContentIssue false
  • English
  • Français

Parallel Tempering Simulation on Generalized Canonical Ensemble

Published online by Cambridge University Press:  20 August 2015

Shun Xu ,
Xin Zhou  and
Zhong-Can Ou-Yang
Shun Xu*
Affiliation:
School of Computer Science and Engineering and Guangdong Key Laboratory of Computer Network, South China University of Technology, Guangzhou 510641, China College of Physical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100190, China Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk 790784, Korea
Xin Zhou*
Affiliation:
College of Physical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100190, China Asia Pacific Center for Theoretical Physics, Pohang, Gyeongbuk 790784, Korea
Zhong-Can Ou-Yang*
Affiliation:
Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
*
Email address:[email protected]
Corresponding author.Email address:[email protected]
Email address:[email protected]
Get access

Abstract

Parallel tempering simulation is widely used in enhanced sampling of systems with complex energy surfaces. We hereby introduce generalized canonical ensemble (GCE) instead of the usual canonical ensemble into the parallel tempering to further improve abilities of the simulation technique. GCE utilizes an adapted weight function to obtain a unimodal energy distribution even in phase-coexisting region and then the parallel tempering on GCE yields the steady swap acceptance rates (SARs) instead of the fluctuated SARs in that on canonical ensemble. With the steady SARs, we can facilitate assign the parameters of the parallel tempering simulation to more efficiently reach equilibrium among different phases. We illustrate the parallel tempering simulation on GCE in the phase-coexisting region of 2-dimensional Potts model, a benchmark system for new simulation method developing. The result indicates that the new parallel tempering method is more efficient to estimate statistical quantities (i.e., to sample the conformational space) than the normal parallel tempering, specially in phase-coexisting regions of larger systems.

Keywords

02.70.Tt05.10.Ln05.50.+qParallel temperinggeneralized canonical ensembleenhanced samplingPotts model
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 5 , November 2012 , pp. 1293 - 1306
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]H., RobertSwendsen and Jian-Sheng Wang, Replica monte carlo simulation of Spin-Glasses, Phys. Rev. Lett., 57(21) (1986), 2607.Google Scholar
[2]Hukushima, Koji and Nemoto, Koji, Exchange monte carlo method and application to spin glass simulations, J. Phys. Soc. Japan, 65(6) (1996), 1604–1608.Google Scholar
[3]Earl, David J. and Deem, Michael W., Parallel tempering: theory, applications and new perspectives, Phys. Chem. Chem. Phys., 7(23) (2005), 3910.Google Scholar
[4]Denschlag, Robert, Martin Lingenheil and Paul Tavan, Optimal temperature ladders in replica exchange simulations, Chem. Phys. Lett., 473(1–3) (2009), 193–195.Google Scholar
[5]Sanbonmatsu, K. Y. and García, A. E., Structure of met-enkephalin in explicit aqueous solution using replica exchange molecular dynamics, Proteins, 46(2) (2002), 225–234, PMID: 11807951.Google Scholar
[6]Patriksson, Alexandra and van der Spoel, David, A temperature predictor for parallel tempering simulations, Phys. Chem. Chem. Phys., 10(15) (2008), 2073.Google Scholar
[7]Kofke, David A., On the acceptance probability of replica-exchange monte carlo trials, J. Chem. Phys., 117(15) (2002), 6911.CrossRefGoogle Scholar
[8]Rathore, Nitin, Chopra, Manan and de Pablo, Juan J., Optimal allocation of replicas in parallel tempering simulations, J. Chem. Phys., 122(2) (2005), 024111.CrossRefGoogle ScholarPubMed
[9]Kone, Aminata and Kofke, David A., Selection of temperature intervals for parallel-tempering simulations, J. Chem. Phys., 122(20) (2005), 206101.CrossRefGoogle ScholarPubMed
[10]Nadler, Walter and Hansmann, Ulrich, Generalized ensemble and tempering simulations: a unified view, Phys. Rev. E, 75(2) (2007), 026109.Google Scholar
[11]Neuhaus, T. and Hager, J., Free-energy calculations with multiple gaussian modified ensembles, Phys. Rev. E, 74(3) (2006), 036702.CrossRefGoogle ScholarPubMed
[12]Challa, Murty S. S. and Hetherington, J. H., Gaussian ensemble: an alternate monte carlo scheme, Phys. Rev. A, 38(12) (1988), 6324–6337.CrossRefGoogle ScholarPubMed
[13]Challa, Murty S. S. and Hetherington, J. H., Gaussian ensemble as an interpolating ensemble, Phys. Rev. Lett., 60(2) (1988), 77–80.Google Scholar
[14]Ray, John R., Microcanonical ensemble monte carlo method, Phys. Rev. A, 44(6) (1991), 4061–4064.Google Scholar
[15]Martin-Mayor, V., Microcanonical approach to the simulation of first-order phase transitions, Phys. Rev. Lett., 98(13) (2007), 137207.Google Scholar
[16]Costeniuc, Marius, Ellis, Richard S., Touchette, Hugo and Turkington, Bruce, The generalized canonical ensemble and its universal equivalence with the microcanonical ensemble, J. Stat. Phys., 119(5) (2005), 1283–1329.Google Scholar
[17]Costeniuc, M., Ellis, R. S., Touchette, H. and Turkington, B., Generalized canonical ensembles and ensemble equivalence, Phys. Rev. E, 73(2) (2006), 026105.CrossRefGoogle ScholarPubMed
[18]Touchette, H., Costeniuc, M., Ellis, R. S. and Turkington, B., Metastability within the generalized canonical ensemble, Phys. A, 365(1) (2006), 132–137.Google Scholar
[19]Velazquez, L. and Curilef, S., Geometrical aspects and connections of the energy-temperature fluctuation relation, J. Phys. A Math. Theor., 42(33) (2009), 335003.CrossRefGoogle Scholar
[20]Velazquez, L. and Curilef, S., A thermodynamic fluctuation relation for temperature and energy, J. Phys. A Math. Theor., 42 (2009), 095006.Google Scholar
[21]Kim, Jaegil and Straub, John E., Optimal replica exchange method combined with tsallis weight sampling, J. Chem. Phys., 130(14) (2009), 144114.Google Scholar
[22]Kim, Jaegil, Keyes, Thomas and Straub, John E., Generalized replica exchange method, J. Chem. Phys., 132(22) (2010), 224107.Google Scholar
[23]Hetherington, J. H. and Stump, Daniel R., Sampling a gaussian energy distribution to study the phase transitions of the z(2) and w(1) lattice gauge theories, Phys. Rev. D, 35(6) (1987), 1972–1978.Google Scholar
[24]Wu, F. Y., The potts model, Rev. Mod. Phys., 54(1) (1982), 235–268.Google Scholar
[25]Lingenheil, Martin, Denschlag, Robert, Mathias, Gerald and Tavan, Paul, Efficiency of exchange schemes in replica exchange, Chem. Phys. Lett., 478(1–3) (2009), 80–84.Google Scholar
[26]Wang, F. and Landau, D. P., Efficient, multiple-range random walk algorithm to calculate the density of states, Phys. Rev. Lett., 86(10) (2001), 2050–2053.CrossRefGoogle ScholarPubMed
[27]Wang, Fugao and Landau, D., Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram, Phys. Rev. E, 64(5) (2001), 056101.CrossRefGoogle ScholarPubMed