Population Annealing and Large Scale Simulations in Statistical Mechanics

  • Lev ShchurEmail author
  • Lev Barash
  • Martin Weigel
  • Wolfhard Janke
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 965)


Population annealing is a novel Monte Carlo algorithm designed for simulations of systems of statistical mechanics with rugged free-energy landscapes. We discuss a realization of the algorithm for the use on a hybrid computing architecture combining CPUs and GPGPUs. The particular advantage of this approach is that it is fully scalable up to many thousands of threads. We report on applications of the developed realization to several interesting problems, in particular the Ising and Potts models, and review applications of population annealing to further systems.


Parallel algorithms Scalability Statistical mechanics Population annealing Markov Chain Monte Carlo Sequential Monte Carlo Hybrid computing architecture CPU+GPGPU 



This work was partially supported by the grant 14-21-00158 from the Russian Science Foundation and by the Landau Institute for Theoretical Physics in the framework of the tasks from the Federal Agency of Scientific Organizations. The authors acknowledge support from the European Commission through the IRSES network DIONICOS under Contract No. PIRSES-GA-2013-612707.


  1. 1.
    Kitaev, A.Yu.: Fault-tolerant quantum computation by anyons. Annals Phys. 303, 2–30 (2003)Google Scholar
  2. 2.
    Iba, Y.: Population Monte Carlo algorithms. Trans. Jpn. Soc. Artif. Intell. 16, 279–286 (2001)CrossRefGoogle Scholar
  3. 3.
    Hukushima, K., Iba, Y.: Population annealing and its application to a spin glass. In: AIP Conference Proceedings, vol. 690, pp. 200–206 (2003)Google Scholar
  4. 4.
    Machta, J.: Population annealing with weighted averages: a Monte Carlo method for rough free-energy landscapes. Phys. Rev. E 82, 026704 (2010)CrossRefGoogle Scholar
  5. 5.
    Weigel, M.: Monte Carlo methods for massively parallel computers. In: Holovatch, Yu. (ed.) Order, Disorder and Criticality, vol. 5, pp. 271–340. World Scientific, Singapore (2018)Google Scholar
  6. 6.
    Barash, L.Yu., Weigel, M., Borovský, M., Janke, W., Shchur, L.N.: GPU accelerated population annealing algorithm. Comp. Phys. Comm. 220, 341–350 (2017)Google Scholar
  7. 7.
    Weigel, M., Barash, L.Yu., Shchur, L.N., Janke, W.: Understanding population annealing Monte Carlo simulations (in preparation)Google Scholar
  8. 8.
    Amey, C., Machta, J.: Analysis and optimization of population annealing. Phys. Rev. E 97, 033301 (2018)CrossRefGoogle Scholar
  9. 9.
    Ferrenberg, A.M., Swendsen, R.H.: Optimized Monte Carlo data analysis. Phys. Rev. Lett. 63, 1195–1198 (1989)CrossRefGoogle Scholar
  10. 10.
    Kumar, S., Bouzida, D., Swendsen, R.H., Kollman, P.A., Rosenberg, J.M.: The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method. J. Comp. Chem. 13, 1011–1021 (1992)CrossRefGoogle Scholar
  11. 11.
    Kumar, S., Rosenberg, J.M., Bouzida, D., Swendsen, R.H., Kollman, P.A.: Mu1tidimensional free-energy calculations using the weighted histogram analysis method. J. Comp. Chem. 16, 1339–1350 (1995)CrossRefGoogle Scholar
  12. 12.
    Code repository for the GPU accelerated PA algorithm is located at:
  13. 13.
    Weigel, M.: Performance potential for simulating spin models on GPU. J. Comput. Phys. 231, 3064–3082 (2012)CrossRefGoogle Scholar
  14. 14.
    Yavors’kii, T., Weigel, M.: Optimized GPU simulation of continuous-spin glass models. Eur. Phys. J. Special Topics 210, 159–173 (2012)CrossRefGoogle Scholar
  15. 15.
    McCool, M., Reinders, J., Robison, A.: Structured Parallel Programming: Patterns for Efficient Computation. Morgan Kaufman, Waltham (2012)Google Scholar
  16. 16.
    Salmon, J.K., Moraes, M.A., Dror, R.O., Shaw, D.E.: Parallel random numbers: as easy as 1, 2, 3. In: Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2011, article no. 16. ACM, New York (2011)Google Scholar
  17. 17.
    Manssen, M., Weigel, M., Hartmann, A.K.: Random number generators for massively parallel simulations on GPU. Eur. Phys. J. Special Topics 210, 53–71 (2012)CrossRefGoogle Scholar
  18. 18.
    Barash, L.Yu., Shchur, L.N.: RNGSSELIB: program library for random number generation, SSE2 realization. Comp. Phys. Comm. 182, 1518–1526 (2011)Google Scholar
  19. 19.
    Barash, L.Yu., Shchur, L.N.: RNGSSELIB: program library for random number generation. More generators, parallel streams of random numbers and Fortran compatibility. Comp. Phys. Comm. 184, 2367–2369 (2013)Google Scholar
  20. 20.
    Guskova, M.S., Barash, L.Yu., Shchur, L.N.: RNGAVXLIB: program library for random number generation, AVX realization. Comp. Phys. Comm. 200, 402–405 (2016)Google Scholar
  21. 21.
    Barash, L.Yu., Shchur, L.N.: PRAND: GPU accelerated parallel random number generation library: using most reliable algorithms and applying parallelism of modern GPUs and CPUs. Comp. Phys. Comm. 185, 1343–1353 (2014)Google Scholar
  22. 22.
    Kramers, H.A., Wannier, G.H.: Statistics of the two-dimensional ferromagnet. Part I. Phys. Rev. 60, 252–262 (1941)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Onsager, L.: Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. 65, 117–149 (1944)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Baxter, R.J.: Potts model at the critical temperature. J. Phys. C Solid State Phys. 6, L445–L448 (1973)CrossRefGoogle Scholar
  25. 25.
    Wu, F.Y.: The Potts model. Rev. Mod. Phys. 54, 235–268 (1982). ibid 55, 315 (1983). ErratumMathSciNetCrossRefGoogle Scholar
  26. 26.
    Binder, K., Heermann, D.: Monte Carlo Simulation in Statistical Physics. Springer, Heidelberg (2010). Scholar
  27. 27.
    Janke, W.: First-order phase transitions. In: Dünweg, B., Landau, D.P., Milchev, A.I. (eds.) Computer Simulations of Surfaces and Interfaces, NATO Science Series, II. Mathematics, Physics and Chemistry, vol. 114, pp. 111–135. Kluwer, Dordrecht (2003)CrossRefGoogle Scholar
  28. 28.
    Borgs, C., Janke, W.: An explicit formula for the interface tension of the 2D Potts model. J. Physique I 2, 2011–2018 (1992)CrossRefGoogle Scholar
  29. 29.
    Barash, L.Yu., Weigel, M., Shchur, L.N., Janke, W.: Exploring first-order phase transitions with population annealing. Eur. Phys. J. Special Topics 226, 595–604 (2017)Google Scholar
  30. 30.
    Borovský, M., Weigel, M., Barash, L.Yu., Žukovič, M.: GPU-accelerated population annealing algorithm: frustrated Ising antiferromagnet on the stacked triangular lattice. In: EPJ Web of Conferences, vol. 108, p. 02016 (2016)Google Scholar
  31. 31.
    Wang, W., Machta, J., Katzgraber, H.G.: Comparing Monte Carlo methods for finding ground states of Ising spin glasses: population annealing, simulated annealing, and parallel tempering. Phys. Rev. E 92, 013303 (2015)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Wang, W., Machta, J., Katzgraber, H.G.: Evidence against a mean-field description of short-range spin glasses revealed through thermal boundary conditions. Phys. Rev. B 90, 184412 (2014)CrossRefGoogle Scholar
  33. 33.
    Wang, W., Machta, J., Katzgraber, H.G.: Chaos in spin glasses revealed through thermal boundary conditions. Phys. Rev. B 92, 094410 (2015)CrossRefGoogle Scholar
  34. 34.
    Wang, W., Machta, J., Munoz-Bauza, H., Katzgraber, H.G.: Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass. Phys. Rev. B 96, 184417 (2017)CrossRefGoogle Scholar
  35. 35.
    Callaham, J., Machta, J.: Population annealing simulations of a binary hard-sphere mixture. Phys. Rev. E 95, 063315 (2017)CrossRefGoogle Scholar
  36. 36.
    Odriozola, G., Berthier, L.: Equilibrium equation of state of a hard sphere binary mixture at very large densities using replica exchange Monte Carlo simulations. J. Chem. Phys. 134, 054504 (2011)CrossRefGoogle Scholar
  37. 37.
    Christiansen, H., Weigel, M., Janke, W.: Population annealing for molecular dynamics simulations of biopolymers. Preprint arXiv:1806.06016

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsChernogolovkaRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.Science Center in ChernogolovkaChernogolovkaRussia
  4. 4.Applied Mathematics Research CentreCoventry UniversityCoventryUK
  5. 5.Institut für Theoretische PhysikUniversität LeipzigLeipzigGermany

Personalised recommendations