Abstract
We present a new algorithm for Monte Carlo simulation of the Ising model. The usual serial architecture of a computer is exploited in a novel way, enabling parallel but independent calculations to be carried out on as many spins as there are bits in a computer word in each fundamental move. The algorithm enjoys a substantial increase in execution speed over more usual multispin coding algorithms. By its very nature, the algorithm constitutes a design for a special-purpose processor.
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References
L. Onsager,Phys. Rev. 65:117 (1944).
Phase Transitions (Cargèse, 1980), M. Lévy, J. C. Le Guillou, and J. Zinn-Justin, eds. (Plenum Press, New York, 1982).
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller,J. Chem. Phys. 22:881 (1954).
L. D. Fosdick,Phys. Rev. 116:565 (1959); L. D. Fosdick, inMethods in Computational Physics, Vol. 1, B. Alder, S. Fernbach, and M. Rotenberg, eds. (Academic Press, New York, 1963).
C. P. Yang,Proceedings of Symposia in Applied Mathematics, Vol. 15, 351 (American Mathematical Society, Providence, Rhode Island, 1963).
Yu. Ya. Gotlib,Fiz. Tverd. Tela 3:2170 (1961) [Sov. Phys.-Solid State 3:1574 (1962)]; R. J. Glauber,J. Math. Phys. 4:294 (1963).
G. F. Mazenko and O. T. Valls,Phys. Rev. B 24:1419 (1981); R. Bausch, V. Dohm, H. K. Janssen, and R. K. P. Zia,Phys. Rev. Lett. 47:1837 (1981).
D. Stauffer,J. Appl. Phys. 53:7980 (1982).
R. B. Pearson, J. L. Richardson, and D. Toussaint,J. Comp. Phys. 51:241 (1983).
A. Hoogland, J. Spaa, B. Selman, and A. Compagner,J. Comp. Phys. 51:250 (1983).
A. F. Bakker, C. Bruin, F. van Dieren, and H. J. Hilhorst,Phys. Lett. 93A:67 (1982).
N. H. Christ and A. E. Terrano,IEEE Trans. Comp. C-33:344 (1984).
R. Friedberg and J. E. Cameron,J. Chem. Phys. 52:6049 (1970).
L. Jacobs and C. Rebbi,J. Comp. Phys. 41:203 (1981).
C. Kalle and V. Winkelmann,J. Stat. Phys. 28:629 (1982), and references therein.
M. P. Harding,J. Comp. Phys. 44:227 (1981).
A. B. Bortz, M. H. Kalos, and J. L. Lebowitz,J. Comp. Phys. 17:10 (1975).
M. H. Kalos, in Proceedings of the Brookhaven Conference on Monte Carlo Methods and Future Computer Architectures, May 1983 (unpublished).
K. E. Schmidt,Phys. Rev. Lett. 51:2175 (1983).
K. G. Wilson,Rev. Mod. Phys. 4:773 (1975).
D. P. Landau,Phys. Rev. B 13:2997 (1976); D. P. Landau,Phys. Rev. B 14:255 (1976).
R. Grishman, “The structure of the PUMA computer system,” Courant Mathematics and Computing Laboratory Report COO-3077-157 (1978).
I. Borosh and H. Niederreiter,BIT 23:65 (1983).
R. C. Tausworthe,Math. Comput. 19:201 (1965).
N. Zierler,Inform. Contr. 15:67 (1969); N. Zierler and J. Brillhart,Inform. Contr. 13:541 (1968); N. Zierler and J. Brillhart,Inform. Contr. 14:566 (1969).
T. G. Lewis and W. H. Payne,J. ACM 20:456 (1973).
H. Niederreiter, inProbability and Statistical Inference, W. Grossman and G. Pflug, eds. (D. Reidel, Dordrecht, 1982).
M. Fushimi and S. Tezuka,Commun. ACM 26:516 (1983).
S. Kirkpatrick and E. P. Stoll,J. Comp. Phys. 40:517 (1981).
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Williams, G.O., Kalos, M.H. A new multispin coding algorithm for Monte Carlo simulation of the Ising model. J Stat Phys 37, 283–299 (1984). https://doi.org/10.1007/BF01011835
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DOI: https://doi.org/10.1007/BF01011835