Skip to main content
Log in

Computer simulations of the Ising Model on Graphics Processing Units

  • Review
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

The aim of this review article is to give an introduction to implementations of the Ising model accelerated by Graphics Processing Units (GPUs) and to summarize different techniques that have been used and tested by different groups. Different parallelization schemes and algorithms are discussed and compared, technical details are pointed out and their performance potential is evaluated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D.P.Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, 2nd edn. (Cambridge University Press, 2005)

  2. J.A.van Meel, A.Arnold, D.Frenkel, S.F.Portegies Zwart, R.G.Belleman, Molecular Simulation 34, 259 (2008)

    Article  Google Scholar 

  3. H.Köstler, R.Schmid, U.Rüde, C.Scheit, Comput. Visualiz. Sci. 11, 115 (2008)

    Article  Google Scholar 

  4. J.J.Schneider, S.Kirkpatrick, Stochastic Optimization (Springer, 2006)

  5. L.Dagum, R.Menon, IEEE Comput. Sci. Eng. 5, 46 (1998)

    Article  Google Scholar 

  6. E.Gabriel, G.E.Fagg, G.Bosilca, T.Angskun, J.J.Dongarra, J.M.Squyres, V.Sahay, P.Kambadur, B.Barrett, A.Lumsdaine, R.H.Castain, D.J.Daniel, R.L.Graham, T.S.Woodall, Proceedings, 11th European PVM/MPI Users’ Group Meeting, 97 (2004)

  7. S.J.Park, J.A.Ross, D.R.Shires, D.A.Richie, B.J.Henz, L.H.Nguyen, IEEE Trans. Parallel Distributed Syst. 22, 46 (2011)

    Article  Google Scholar 

  8. A.Ruiz, M.Ujaldon, L.Cooper, K.Huang, J. Signal Proc. Syst. Signal Image Video 55, 229 (2009)

    Article  Google Scholar 

  9. O.M.Lozano, K.Otsuka, J. Signal Proc. Syst. Signal Image Video 57, 285 (2009)

    Article  Google Scholar 

  10. A.C.Thompson, C.J.Fluke, D.G.Barnes, B.R.Barsdell, New Astronomy 15, 16 (2010)

    Article  ADS  Google Scholar 

  11. E.B.Ford, New Astronomy 14, 406 (2009)

    Article  ADS  Google Scholar 

  12. R.B.Wayth, L.J.Greenhill, F.H.Briggs, Publ. Astron. Soc. Pac. 121, 857 (2009)

    Article  ADS  Google Scholar 

  13. R.G.Belleman, J.Bedorf, S.F.P.Zwart, New Astronomy 13, 103 (2008)

    Article  ADS  Google Scholar 

  14. I.S.Haque, V.S.Pande, J. Comput. Chem. 31, 117 (2010)

    Article  Google Scholar 

  15. N.Schmid, M.Botschi, W.F.Van Gunsteren, J. Comput. Chem. 31, 1636 (2010)

    Google Scholar 

  16. J.E.Stone, J.C.Phillips, P.L.Freddolino, D.J.Hardy, L.G.Trabuco, K.Schulten, J. Comput. Chem. 28, 2618 (2007)

    Article  Google Scholar 

  17. V.B.Putz, J.Dunkel, J.M.Yeomans, Chem. Phys. 375, 557 (2010)

    Article  ADS  Google Scholar 

  18. S.Tomov, M.McGuigan, R.Bennett, G.Smith, J. Spiletic, Comput. Graph. 29, 71 (2005)

    Article  Google Scholar 

  19. E.Gutierrez, S.Romero, M.A.Trenas, E.L.Zapata, Comput. Phys. Commun. 181, 283 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. F.Molnar, T.Szakaly, R.Meszaros, I.Lagzi, Comput. Phys. Commun. 181, 105 (2010)

    Article  ADS  MATH  Google Scholar 

  21. K.Hagiwara, J.Kanzaki, N.Okamura, D.Rainwater, T.Stelzer, Eur. Phys. J. C 66, 477 (2010)

    Article  ADS  Google Scholar 

  22. S.Bianchi, R.Di Leonardo, Comput. Phys. Commun. 181, 1442 (2010)

    Article  ADS  Google Scholar 

  23. B.Block, P.Virnau, T.Preis, Comput. Phys. Commun. 181, 1549 (2010)

    Article  ADS  MATH  Google Scholar 

  24. D.Komatitsch, G.Erlebacher, D.Goddeke, D.Michea, J. Comput. Phys. 229, 7692 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. S.Rostrup, H.De Sterck, Comput. Phys. Commun. 181, 2164 (2010)

    Article  ADS  MATH  Google Scholar 

  26. T.Preis, P.Virnau, W.Paul, J.J.Schneider, J. Comput. Phys. 228, 4468 (2009)

    Article  ADS  MATH  Google Scholar 

  27. N.Sanna, I.Baccarelli, G.Morelli, Comput. Phys. Commun. 180, 2544 (2009)

    Article  ADS  MATH  Google Scholar 

  28. J.A.Anderson, C.D.Lorenz, A.Travesset, J. Comput. Phys. 227, 5342 (2008)

    Article  ADS  MATH  Google Scholar 

  29. T.Preis, P.Virnau, W.Paul, J.J.Schneider, New J. Phys. 11, 093024 (2009)

    Article  ADS  Google Scholar 

  30. T.Preis, W.Paul, J.J.Schneider, Europhys. Lett. 82, 68005 (2008)

    Article  ADS  Google Scholar 

  31. T.Preis, Eur. Phys. J. Special Topics 194, 5 (2011)

    Article  ADS  Google Scholar 

  32. T.Preis, Eur. Phys. J. Special Topics 194, 87 (2011)

    Article  ADS  Google Scholar 

  33. H.E.Stanley, et al., Physica A 389, 2880 (2010)

    Article  ADS  Google Scholar 

  34. D.Michea, D.Komatitsch, Geophysical J. Int. 182, 389 (2010)

    ADS  Google Scholar 

  35. X.K.Zhang, X.Zhang, Z.H.Zhou, J. Struct. Biol. 172, 400 (2010)

    Article  Google Scholar 

  36. D.Castano-Diez, D.Moser, A.Schoenegger, S.Pruggnaller, A.S.Frangakis, J. Struct. Biol. 164, 153 (2008)

    Article  Google Scholar 

  37. D.Dynerman, E.Butzlaff, J.C.Mitchell, J. Comput. Biol. 16, 523 (2009)

    Article  Google Scholar 

  38. J.Buckner, J.Wilson, M.Seligman, B.Athey, S.Watson, F.Meng, Bioinformatics 26, 134 (2010)

    Article  Google Scholar 

  39. J.M.Cecilia, J.M.Garcia, G.D.Guerrero, M.A.Martinez-del Amor, I.Perez-Hurtado, M.J.Perez-Jimenez, Briefings Bioinform. 11, 313 (2010)

    Article  Google Scholar 

  40. L.Dematte, D.Prandi, Briefings Bioinform. 11, 323 (2010)

    Article  Google Scholar 

  41. P.B.Noel, A.M.Walczak, J.H.Xu, J.J.Corso, K.R.Hoffmann, S.Schafer, Comput. Meth. Progr. Biomed. 98, 271 (2010)

    Article  Google Scholar 

  42. W.F.Shen, D.M.Wei, W.M.Xu, X.Zhu, S.Z.Yuan, Comput. Meth. Progr. Biomed. 100, 87 (2010)

    Article  Google Scholar 

  43. J.C.Phillips, J.E.Stone, Commun. ACM 52, 34 (2009)

    Article  Google Scholar 

  44. S.Hissoiny, B.Ozell, P.Despres, Med. Phys. 37, 1029 (2010)

    Article  Google Scholar 

  45. C.Rohkohl, B.Keck, H. G.Hofmann, J.Hornegger, Med. Phys. 36, 3940 (2009)

    Article  Google Scholar 

  46. M.de Greef, J.Crezee, J.C.van Eijk, R.Pool, A.Bel, Med. Phys. 36, 4095 (2009)

    Article  Google Scholar 

  47. C.H.Men, X.J.Gu, D.J.Choi, A.Majumdar, Z.Y.Zheng, K.Mueller, S.B.Jiang, Phys. Med. Biol. 54, 6565 (2009)

    Article  Google Scholar 

  48. A.Badal, A.Badano, Med. Phys. 36, 4878 (2009)

    Article  Google Scholar 

  49. S.S.Samant, J.Y.Xia, P.Muyan-Ozcelilk, J.D.Owens, Med. Phys. 35, 3546 (2008)

    Article  Google Scholar 

  50. Z.A.Taylor, O.Comas, M.Cheng, J.Passenger, D.J.Hawkes, D.Atkinson, S.Ourselin, Med. Image Anal. 13, 234 (2009)

    Article  Google Scholar 

  51. K.Xu, D.Z.Ding, Z.H.Fan, R.S.Chen, Micr. Opt. Technol. Lett. 52, 502 (2010)

    Article  Google Scholar 

  52. V.Demir, A.Z.Elsherbeni, Appl. Comput. Electromagn. Soc. J. 25, 303 (2010)

    Google Scholar 

  53. V.Demir, Appl. Comput. Electromagn. Soc. J. 25, 323 (2010)

    Google Scholar 

  54. N.Godel, N.Nunn, T.Warburton, M.Clemens, Appl. Comput. Electromagn. Soc. J. 25, 331 (2010)

    Google Scholar 

  55. F.Rossi, C.McQuay, P.So, Appl. Comput. Electromagn. Soc. J. 25, 348 (2010)

    Google Scholar 

  56. A.Capozzoli, C.Curcio, G.DÉlia, A.Liseno, P.Vinetti, Appl. Comput. Electromagn. Soc. J. 25, 355 (2010)

    Google Scholar 

  57. N.Godel, S.Schomann, T.Warburton, M.Clemens, IEEE Trans. Magn. 46, 2735 (2010)

    Article  ADS  Google Scholar 

  58. N.Godel, N.Nunn, T.Warburton, M.Clemens, IEEE Trans. Magn. 46, 3469 (2010)

    Article  ADS  Google Scholar 

  59. J.M.Nageswaran, N.Dutt, J.L.Krichmar, A.Nicolau, A.V.Veidenbaum, Neural Networks 22, 791 (2009)

    Article  Google Scholar 

  60. Y.C.Liu, B.Schmidt, W.G.Liu, D.L.Maskell, Pattern Recogn. Lett. 31, 2170 (2010)

    Article  Google Scholar 

  61. A.Munawar, M.Wahib, M.Munetomo, K.Akama, Genetic Progr. Evolvable Mach. 10, 391 (2009)

    Article  Google Scholar 

  62. C.Muller, S.Frey, M.Strengert, C.Dachsbacher, T.Ertl, IEEE Trans. Visualiz. Comp. Graph. 15, 605 (2009)

    Article  Google Scholar 

  63. C.Wan, Y.J.Chiang, IEEE Trans. Visualiz. Comput. Graph. 15, 1367 (2009)

    Article  Google Scholar 

  64. D.M.Hughes, I.S.Lim, IEEE Trans. Visualiz. Comput. Graph. 15, 1555 (2009)

    Article  Google Scholar 

  65. A.Godiyal, J.Hoberock, M.Garland, J.C.Hart, I.G.E.D.Tollis, M.Patrignani, Graph Drawing 5417, 90 (2009)

    Article  Google Scholar 

  66. D.Goddeke, R.Strzodka, IEEE Trans. Parallel Distrib. Syst. 22, 22 (2011)

    Article  Google Scholar 

  67. J.Nickolls, W.J. Dally, IEEE Micro 30, 56 (2010)

    Article  Google Scholar 

  68. A.Benso, S.Di Carlo, G.Politano, A.Savino, A.Scionti, Control Eng. Appl. Inform. 12, 34 (2010)

    Google Scholar 

  69. K.Jang, S.Han, S.Han, S.Moon, K.Park, Comput. Comm. Rev. 40, 437 (2010)

    Google Scholar 

  70. A.Akoglu, G.M.Striemer, Cluster Computing-The J. Networks Software Tools Appl. 12, 341 (2009)

    Google Scholar 

  71. A.Leist, D.P.Playne, K.A.Hawick, Concurr. Comput. Pract. Exper. 21, 2400 (2009)

    Article  Google Scholar 

  72. M.Garland, S.Le Grand, J.Nickolls, J.Anderson, J.Hardwick, S.Morton, E.Phillips, Y.Zhang, V.Volkov, IEEE Micro 28, 13 (2008)

    Article  Google Scholar 

  73. S.S.Stone, J.P.Haldar, S.C.Tsao, W.M.W.Hwu, B.P.Sutton, Z.P.Liang, J. Parallel Distrib. Comput.68, 1307 (2008)

    Article  Google Scholar 

  74. S.Che, M.Boyer, J.Y.Meng, D.Tarjan, J.W.Sheaffer, K.Skadron, J. Parallel Distrib. Comput.68, 1370 (2008)

    Article  Google Scholar 

  75. T.Levy, G.Cohen, E.Rabani, J. Chem. Theor. Comput. 6, 3293 (2010)

    Article  Google Scholar 

  76. E.E.Ferrero, J.P.De Francesco, N.Wolovick, S.A.Cannas, q-State Potts Model Metastability Study Using Optimized GPU-Based Monte Carlo Algorithms (2011), preprint [arXiv:1101.0876]

  77. K.Hawick, A.Leist, D.Playne, Int. J. Parallel Progr. 39, 183 (2011)

    Article  Google Scholar 

  78. V.Demchik, A.Strelchenko, Monte Carlo simulations on Graphics Processing Units (2009), preprint [arXiv:0903.3053]

  79. J.Yin, D.P.Landau, Phys. Rev. E 80, 051117 (2009)

    Article  ADS  Google Scholar 

  80. E.Ising, Z. Phys. 31, 253 (1925)

    Article  ADS  Google Scholar 

  81. N.Metropolis, A.W.Rosenbluth, M.N.Rosenbluth, A.H.Teller, E.Teller, J. Chem. Phys. 21, 1087 (1953)

    Article  ADS  Google Scholar 

  82. B. A.Berg, Markov Chain Monte Carlo Simulations and Their Statistical Analysis (World Scientific Publishing, 2004)

  83. N.Ito, Y.Kanada, Supercomputer 5, 31 (1988)

    Google Scholar 

  84. U.Wolff, Phys. Rev. Lett. 62, 361 (1989)

    Article  ADS  Google Scholar 

  85. R.H.Swendsen, J.S.Wang, Phys. Rev. Lett. 58, 86 (1987)

    Article  ADS  Google Scholar 

  86. J.Kaupuzs, J.Rimsans, R.V.N.Melnik, Phys. Rev. E 81, 026701 (2010)

    Article  ADS  Google Scholar 

  87. Y.Komura, Y.Okabe, J. Computat. Phys. 231, 1209 (2012)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  88. M.Weigel, Phys. Rev. E 84, 036709 (2011)

    Article  ADS  Google Scholar 

  89. M.Weigel, J. Comput. Phys. 231, 3064 (2012)

    Google Scholar 

  90. Y.Komura, Y.Okabe Comput. Phys. Commun. 183, 1155 (2012)

    Article  ADS  Google Scholar 

  91. J.Hoshen, R.Kopelman, Phys. Rev. B 14, 73438 (1976)

    Article  ADS  Google Scholar 

  92. M.Matsumoto, M.Saito, H.Haramoto, T.Nishimura, J. Univ. Comput. Sci. 12, 672 (2006)

    MathSciNet  Google Scholar 

  93. W.H.Press, S.A.Teukolsky, W.T.Vetterling, B.P.Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, Cambridge, 2007)

  94. H.Nguyen, GPU Gems 3 (Addison-Wesley Professional, August 2007)

  95. R.C.Tausworthe, Math. Comput. 201 (1965)

  96. S.Wansleben, J.G.Zabolitzky, C.Kalle, J. Stat. Phys. 37, 271 (1984)

    Article  ADS  Google Scholar 

  97. R.Zorn, H.J.Herrmann, C.Rebbi, Comput. Phys. Commun. 23, 337 (1981)

    Article  ADS  Google Scholar 

  98. M.Bernaschi, M.Fatica, G.Parisi, L.Parisi, Comput. Phys. Commun. 183, 1416 (2012)

    Article  ADS  Google Scholar 

  99. M.Manssen, M.Weigel, A.K.Hartmann, Eur. Phys. J. Specical Topics 210, 53 (2012)

    Article  Google Scholar 

  100. N.Ito, Y.Kanada, Supercomputer 7, 29 (1990)

  101. A.T.Ogielski, Phys. Rev. B 36, 7315 (1987)

    Article  ADS  Google Scholar 

  102. D.Stauffer, Physica A 244, 344 (1997)

    Article  ADS  Google Scholar 

  103. M.Weigel, Comput. Phys. Commun. 82, 1833 (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to B. J. Block or T. Preis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Block, B.J., Preis, T. Computer simulations of the Ising Model on Graphics Processing Units. Eur. Phys. J. Spec. Top. 210, 133–145 (2012). https://doi.org/10.1140/epjst/e2012-01642-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2012-01642-y

Keywords

Navigation