Monte Carlo Simulations of the Ising Model on GPU
Wojtkiewicz Jacek 1*, Kalinowski Krzysztof 2
1 Departmentfor Mathematical Methods in Physics
Faculty of Physics,University of Warsaw
ul. Pasteura 5,02-093 Warszawa, Poland
*E-mail: wjacek@fuw.edu.pl2 R.D.Labs,Sp. z o.o.
ul. Ho ̇za 43/49m. 11,00-681Warszawa,Poland
Received:
Received:18 June 2014; revised:17 March 2015;accepted:21 April 2015; published online:15 June 2015
DOI: 10.12921/cmst.2015.21.02.003
Abstract:
Monte Carlo simulations of two- and three-dimensional Ising model on graphic cards (GPU) are described. The standard Metropolis algorithm has been employed. In the framework of the implementation developed by us, simulations were up to 100 times faster than their sequential CPU analogons. It is possible to perform simulations for systems containing up to 10^9 spins on Tesla C2050 GPU. As a physical application, higher cumulants for the 3d Ising model have been calculated.
Key words:
References:
[1] nVidia, NVIDIA CUDA C Programming Guide by nVidia
Corporation http://developer.download.nvidia.com/compute/-
DevZone/docs/html/C/doc/CUDACProgramming Guide.pdf
[2] nVidia, CUDAC Best Practices Guide by nVidia Corpora-
tion http://developer.download.nvidia.com/compute/DevZone/
docs/html/C/doc/CUDA C BestPractices Guide.pdf
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228 (2009)
[4] M.Weigel, Comp. Phys.Comm. 182,1833(2011)
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CUDA http://www.physik.uni-leipzig.de/bordag/GCC/Talks/
Wende.pdf
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The Theory of Critical Phenomena. An Introduction to the
Renormalization Group. Clarendon Press, Oxford 1992.
[7] J. Glimm, A. Jaffe: Quantum Physics – A Functional Integral Point Of View. Springer-Verlag,New York – Heidelberg-
Berlin1981.
[8] J. R. Baxter,Exactly Solved Models in Statistical Mechanics,
Academic Press,1989
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ewit, Y.T. J. C.Fonk,J.R. Heringa,A. HooglandandA. L.
van Willigen, Europhys. Lett. 10, 105(1989).
[21] A. Rosengren,J.Phys. A 19,1709 (1986).
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Chinese Physics C36, 727 (2012)
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Critical Phenomena vol. 8, C. Domb and J. Lebowitz,Eds.,
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[29] Ch. Gruber, N. Macris:Helv.Phys. Acta69,850(1996).
[30] W. Selke: Phys.Reports 170,213 (1988).
Monte Carlo simulations of two- and three-dimensional Ising model on graphic cards (GPU) are described. The standard Metropolis algorithm has been employed. In the framework of the implementation developed by us, simulations were up to 100 times faster than their sequential CPU analogons. It is possible to perform simulations for systems containing up to 10^9 spins on Tesla C2050 GPU. As a physical application, higher cumulants for the 3d Ising model have been calculated.
Key words:
References:
[1] nVidia, NVIDIA CUDA C Programming Guide by nVidia
Corporation http://developer.download.nvidia.com/compute/-
DevZone/docs/html/C/doc/CUDACProgramming Guide.pdf
[2] nVidia, CUDAC Best Practices Guide by nVidia Corpora-
tion http://developer.download.nvidia.com/compute/DevZone/
docs/html/C/doc/CUDA C BestPractices Guide.pdf
[3] T.Preis, P.Virnau, W. Paul, J. J. Schneider:J.Comp. Phys.
228 (2009)
[4] M.Weigel, Comp. Phys.Comm. 182,1833(2011)
[5] F. Wende, Implementation of the 2D Ising Model using
CUDA http://www.physik.uni-leipzig.de/bordag/GCC/Talks/
Wende.pdf
[6] J. J.Binney, N. J. Dowrick, A.J. Fisher,M.E. J. Newman:
The Theory of Critical Phenomena. An Introduction to the
Renormalization Group. Clarendon Press, Oxford 1992.
[7] J. Glimm, A. Jaffe: Quantum Physics – A Functional Integral Point Of View. Springer-Verlag,New York – Heidelberg-
Berlin1981.
[8] J. R. Baxter,Exactly Solved Models in Statistical Mechanics,
Academic Press,1989
[9] E.Luijten, Ph.D. Thesis, Delft University 1997.
[10] H. W. J.Blöte,E. Luijtenand J.R. Heringa, J. Phys.A28,
6289 (1995).
[11] P.Butera, M.Comi,Phys. Rev. B 56,8212(1997).
[12] A. L.Talapov, H. W. J. Blöte, J. Phys.A29, 5727(1996).
[13] R. Gupta, P.Tamayo,Int. J. Mod.Phys. C 7, 305 (1996).
[14] D. P. Landau, Physica A 205, 41(1994).
[15] H. W. J.Blöte, G. Kamieniarz, Physica A 196, 455 (1993).
[16] C. F. Baillie, R.Gupta, K.A. Hawickand G. S. Pawley,Phys.
Rev. B 45,10438 (1992).
[17] F. Livet, Europhys. Lett. 16,139 (1991).
[18] A. M. Ferrenberg and D.P. Landau, Phys.Rev. B 44, 5081
(1991).
[19] N. Ito, M.Suzuki, J. Phys.Soc.Jpn. 60, 1978 (1991).
[20] H. W. J. Blöte, J. A. deBruin,A.Compagner, J. H.Croock-
ewit, Y.T. J. C.Fonk,J.R. Heringa,A. HooglandandA. L.
van Willigen, Europhys. Lett. 10, 105(1989).
[21] A. Rosengren,J.Phys. A 19,1709 (1986).
[22] V. Privman, P.C. Hohenberg and A. Aharony: Universal
Critical-Point Amplitude Relations.In:Phase Transitions and
Critical Phenomena vol.14, C.Domband J. Lebowitz,Eds.,
Academic Press 1991.
[23] W. Selkeand, L.S. Shchur, J.Phys. A 38, L739(2005).
[24] W. Selke, Europhys. J. B51, 223 (2006).
[25] J. Salas, A.D. Sokal,J.Stat. Phys.98,551(2000).
[26] Chen Li Zhu,Pan Xue, Chen XiaoSong,Wu Yuan Fang:
Chinese Physics C36, 727 (2012)
[27] M.N. Barber: Finite Size Scaling. In: Phase Transitions and
Critical Phenomena vol. 8, C. Domb and J. Lebowitz,Eds.,
Academic Press 1983.
[28] L.M. Falicov, J.C. Kimball: Phys.Rev.Lett. 22,997(1969).
[29] Ch. Gruber, N. Macris:Helv.Phys. Acta69,850(1996).
[30] W. Selke: Phys.Reports 170,213 (1988).
