Fractal geometry of critical Potts clusters
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Numerical simulations on the total mass, the numbers of bonds on the hull, external perimeter, singly connected bonds and gates into large fjords of the Fortuin-Kasteleyn clusters for two-dimensional q-state Potts models at criticality are presented. The data are found consistent with the recently derived corrections-to-scaling theory. A new method for thermalization of spin systems is presented. The method allows a speed up of an order of magnetization for large lattices. We also show snapshots of the Potts clusters for different values of q, which clearly illustrate the fact that the clusters become more compact as q increases, and that this affects the fractal dimensions in a monotonic way. However, the approach to the asymptotic region is slow, and the present range of the data does not allow a unique identification of the exact correction exponents.
KeywordsHull Fractal Dimension Total Mass Potts Model Spin System
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- 6.E. Ising, Z. Phys. 21, 613 (1925)Google Scholar
- 10.D. Stauffer, A. Aharony, Introduction to Percolation Theory, revised 2nd edition ed. (Taylor and Francis, Burgess Science Press, Basingstoke, London, 1994)Google Scholar
- 13.R. Pike, H.E. Stanley, J. Phys. A 14, L169 (1981)Google Scholar
- 14.B.B. Mandelbrot, The Fractal Geometry of Nature (W.H. Freedman and Company, New York, 1977)Google Scholar
- 15.R.F. Voss, J. Phys. A 17, L373 (1984)Google Scholar
- 16.A. Bunde, J.F. Gouyet, J. Phys. A 18, L285 (1985)Google Scholar
- 17.T. Grossman, A. Aharony, J. Phys. A 19, L745 (1986)Google Scholar
- 21.A. Aharony, J. Asikainen, in Scaling and Disordered Systems, edited by F. Family, M. Daoud, H.J. Herrmann, H.E. Stanley (World Scientific, Singapore, 2002)Google Scholar
- 22.N. Metropolis , J. Chem. Phys 21, 1087 (1953)Google Scholar
- 29.J. Hoshen, R. Kopelman, Phys. Rev. B 14, 3438 (1976)Google Scholar
- 30.W.H. Press, S.A. Teukolsky, W.T.V.B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Great Britain, Cambridge, 1992)Google Scholar