Bond-updating mechanism in cluster Monte Carlo calculations

J. R. Heringa; H. W. J. Blöte

doi:10.1103/PhysRevE.49.R1827

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Bond-updating mechanism in cluster Monte Carlo calculations

J. R. Heringa and H. W. J. Blöte

Faculty of Applied Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

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Phys. Rev. E 49, R1827(R) – Published 1 March, 1994

DOI: https://doi.org/10.1103/PhysRevE.49.R1827

Abstract

We study a cluster Monte Carlo method with an adjustable parameter: the number of energy levels of a demon mediating the exchange of bond energy with the heat bath. The efficiency of the algorithm in the case of the three-dimensional Ising model is studied as a function of the number of such levels. The optimum is found in the limit of an infinite number of levels, where the method reproduces the Wolff or the Swendsen-Wang algorithm. In this limit the size distribution of flipped clusters approximates a power law more closely than that for a finite number of energy levels.

References (19)

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P.W. Kasteleyn and C.M. Fortuin,, J. Phys. Soc. Jpn. 46, (Suppl.) 11 (1969).
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J.R. Heringa and H.W.J. Blöte, Phys. Rev. Lett. 70, 2044 (1993).
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[c1] N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller and E. Teller, J. Chem. Phys. 21, 1087 (1953).

[c2] P.W. Kasteleyn and C.M. Fortuin,, J. Phys. Soc. Jpn. 46, (Suppl.) 11 (1969).

[c3] R.H. Swendsen and J. S. Wang, Phys. Rev. Lett. 58, 86 (1987).

[c4] C. K. Hu, Phys. Rev. B 29, 5103 (1984); ibid. 46, 6592 (1992).

[c5] J.R. Heringa and H.W.J. Blöte, Phys. Rev. Lett. 70, 2044 (1993).

[c6] M. Creutz, Phys. Rev. Lett. 69, 1002 (1992).

[c7] K. Kawasaki, in Phase Transitions and Critical Phenomena, edited by C. Domb and M.S. Green (Academic, New York, 1972), Vol. 2.

[c8] M. Creutz, Phys. Rev. Lett. 50, 1411 (1983).

[c9] M.S.S. Challa and J.H. Hetherington, Phys. Rev. Lett. 60, 77 (1988).

[c10] R.W. Gerling and A. Hüller, Z. Phys. B 90, 207 (1993).

[c11] L.D. Fosdick, Phys. Rev. 116, 565 (1959).

[c12] C. P. Yang, Proc. Symp. Appl. Math. 15, 351 (1963).

[c13] C. Münkel, D.W. Heermann, J. Adler, M. Gofman and D. Stauffer, Physica A 193, 540 (1993).

[c14] D. Kandel, R. Ben Av and E. Domany, Phys. Rev. Lett. 65, 941 (1990); D. Kandel and E. Domany, Phys. Rev. B 43, 8539 (1991).

[c15] V.B. Andreichenko, Pis'ma Zh. Eksp. Teor. Fiz. 57, 732 (1993) [JETP Lett. 57, 744 (1993)].

[c16] W. Kerler, Phys. Rev. D 47, 1285 (1993).

[c17] U. Wolff, Phys. Rev. Lett. 62, 361 (1989).

[c18] C.F. Baillie, R. Gupta, K.A. Hawick and G.S. Pawley, Phys. Rev. B 45, 10438 (1992) H.W.J. Blöte and G. Kamieniarz, Physica A 196, 455 (1993).

[c19] C. Ruge and F. Wagner, J. Stat. Phys. 66, 99 (1992).

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Bond-updating mechanism in cluster Monte Carlo calculations

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References (19)

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