GPU-based single-cluster algorithm for the simulation of the Ising model

Journal of Computational Physics

Volumn 231, Issue 4, 2012, Pages 1209-1215

  Komura, Yukihiro ^a   Okabe, Yutaka ^a  

^a TOKYO METROPOLITAN UNIVERSITY   (Japan)

Author keywords

Cluster algorithm; GPU; Ising model; Monte Carlo simulation; Parallel computing

Indexed keywords

CLUSTER COMPUTING; CLUSTERING ALGORITHMS; INTELLIGENT SYSTEMS; ISING MODEL; MONTE CARLO METHODS; SYNCHRONIZATION;

BLOCK SYNCHRONIZATION; CALCULATION SPEED; CLUSTER ALGORITHMS; CLUSTER MONTE CARLO; CRITICAL TEMPERATURES; DEVICE ARCHITECTURES; MONTE CARLO'S SIMULATION; PARALLEL COM- PUTING; PARALLEL COMPUTATION; TWO-DIMENSIONAL ISING MODEL;

GRAPHICS PROCESSING UNIT;

EID: 84855206756     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.09.029     Document Type: Article

References (24)

1. Onsager L. Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. 1944, 65:117-149.
2. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. Equation of state calculations by fast computing machines. J. Chem. Phys. 1953, 21:1087-1092.
3. Swendsen R.H., Wang J.S. Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett. 1987, 58:86-88.
4. Wolff U. Collective Monte Carlo updating for spin systems. Phys. Rev. Lett. 1989, 62:361-364.
5. Wang F., Landau D.P. Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 2001, 86:2050-2053.
6. Ufimtsev I.S., Martinez T.J. Quantum chemistry on graphical processing units. 1. Strategies for two-electron integral evaluation. J. Chem. Theory Comput. 2008, 4:222-231.
7. Anderson J.A., Lorenz C.D., Travesset A. General purpose molecular dynamics simulations fully implemented on graphics processing units. J. Comput. Phys. 2008, 227:5342-5359.
8. Sunarso A., Tsuji T., Chono S. GPU-accelerated molecular dynamics simulation for study of liquid crystalline flows. J. Comput. Phys. 2010, 229:5486-5497.
9. Kuttera O., Shams R., Navab N. Visualization and GPU-accelerated simulation of medical ultrasound from CT images. Comput. Methods Programs Biomed. 2009, 94:250-266.
10. H. Scherl, B. Keck, M. Kowarschik, J. Hornegger, Fast GPU-based CT reconstruction using the common unified device architecture (CUDA), in: IEEE Nuclear Science Symposium Conference Record, vol. 6, 2007, pp. 4464-4466.
11. Preis T., Virnau P., Paul W., Schneider J.J. Accelerated fluctuation analysis by graphic cards and complex pattern formation in financial markets. New J. Phys. 2009, 11:093024.
12. Preis T., Virnau P., Paul W., Schneider J.J. GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model. J. Comput. Phys. 2009, 228:4468-4477.
13. Block B., Virnau P., Preis T. Multi-GPU accelerated multi-spin Monte Carlo simulations of the 2D Ising model. Comput. Phys. Commun. 2010, 181:1549-1556.
14. Bae S., Ko S.H., Coddington P.D. Parallel Wolff cluster algorithms. Int. J. Mod. Phys. C 1995, 6:197-210.
15. Kaupuzs J., Rimsans J., Melnik R.V.N. Parallelization of the Wolff single-cluster algorithm. Phys. Rev. E 2010, 81:026701.
16. Janke W. Monte Carlo simulations of spin systems. Computational Physics 1996, 10-43. Springer, Berlin. K.H. Hoffmann, M. Schreiber (Eds.).
17. Landau D.P., Binder K. A guide to Monte Carlo simulations in statistical physics 2005, Cambridge University Press, Cambridge. second ed.
18. S. Xiao, W. Feng, Inter-block GPU communication via fast barrier synchronization, in: Proceedings of the IEEE International Parallel and Distributed Processing Symposium, April 2010, pp. 1-12.
19. Volkov V., Demmel J.W. Benchmarking GPUs to tune dense linear algebra. Proceedings of the 2008 ACM/IEEE Conference on Supercomputing 2008, 1-11. IEEE Press.
20. Evertz H.G., Lana G., Marcu M. Cluster algorithm for vertex models. Phys. Rev. Lett. 1993, 70:875-879.
21. Kawashima N., Gubernatis J.E. Loop algorithms for Monte Carlo simulations of quantum spin systems. Phys. Rev. Lett. 1994, 73:1295-1298.
22. Beard B.B., Wiese U.-J. Simulations of discrete quantum systems in continuous Euclidean time. Phys. Rev. Lett. 1996, 77:5130-5133.
23. Tomita Y., Okabe Y. Probability-changing cluster algorithm for Potts models. Phys. Rev. Lett. 2001, 86:572-575.
24. K.A. Hawick, A. Leist, D.P. Playne, Cluster and fast-update simulations of regular and rewired lattice Ising models using CUDA and graphical processing units, Technical Report CSTN-104, 2010.