Abstract
Topological properties of clusters are used to extract critical parameters. This method is tested for the bulk properties ofd=2 percolation and thed=2, 3 Ising model. For the latter we obtain an accurate value of the critical temperatureJ/k B T c=0.221617(18). In the case of thed=3 Ising model with film geometry the critical value of the surface coupling at the special transitions is determined as J1c/J=1.5004(20) together with the critical exponents β m1 =0.237(5) andϕ=0.461(15).
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References
H. W. Diehl, inPhase Transitions and Critical Phenomena, Vol. 10, C. Domb and J. Lebowitz, eds. (Academic Press, London, 1986).
K. Binder and P. C. Hohenberg,Phys. Rev. B 6:3461 (1972); 9:2194 (1974).
D. P. Landau and K. Binder,Phys. Rev. B 41:4633 (1990).
M. Kikuchi and Y. Okabe,Prog. Theor. Phys. 73:32 (1985).
K. Binder, inPhase Transitions and Critical Phenomena, Vol. 3, C. Domb and M. S. Green, eds. (Academic Press, London, 1976), p. 1.
R. H. Swendsen and J. S. Wang,Phys. Rev. Lett. 58:86 (1987).
U. Wolff,Phys. Rev. Lett. 62:361 (1989).
M. D. De Meo, D. W. Heermann, and K. Binder,J. Stat. Phys. 60:585 (1990).
C. Ruge and F. Wagner,J. Stat. Phys. 66:99 (1992).
P. J. Reynolds, H. E. Stanley, and W. Klein,Phys. Rev. B 21:1223 (1980).
K. Binder,Z. Phys. B 43:119 (1981).
P. W. Kasteleyn and C. M. Fortuin,Phys. Soc. Jpn. 26(suppl.):11 (1969).
C. Domb, inPhase Transitions and Critical Phenomena, Vol. 3, C. Domb and M. S. Green, eds. (Academic Press, London, 1974), p. 357.
C. Ruge, S. Dunkelmann, and F. Wagner,Phys. Rev. Lett. 69:2465 (1992).
F. T. Wu,Rev. Mod. Phys. 54:235 (1982).
U. Wolff,Nucl. Phys. B 300 [FS22]:501 (1988).
L. de Arcangelis,J. Phys. A 20:3057 (1987).
Stauffer,Introduction to Percolation Theory (Taylor & Francis, 1985).
J. Hoshen and R. Kopelman,Phys. Rev. B 27:3438 (1976).
P. L. Leath,Phys. Rev. B 14:5046 (1976).
J. S. Wang and R. H. Swendsen,Physica A 167:567 (1990).
P. Tamajo, R. C. Brower, and W. Klein,J. Stat. Phys. 60:889 (1990).
U. Wolff,Nucl. Phys. B 334:581 (1990).
A. Liu and M. E. Fisher,Physica A 156:35 (1989).
G. S. Pawley, R. H. Swendsen, D. J. Wallace, and K. G. Wilson,Phys. Rev. B 29:4030 (1984).
C. F. Baillie, R. Gupta, K. A. Hawick, and C. S. Pawley,Phys. Rev. B 45:10438 (1992).
A. M. Ferrenberg and D. P. Landau,Phys. Rev. B 44:5081 (1991).
C. Ruge, S. Dunkelmann, F. Wagner, and J. Wulf, to be published.
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Ruge, C., Dunkelmann, S., Wagner, F. et al. Study of the three-dimensional Ising model on film geometry with the cluster Monte Carlo method. J Stat Phys 73, 293–317 (1993). https://doi.org/10.1007/BF01052762
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DOI: https://doi.org/10.1007/BF01052762