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VOLUME 75 | ISSUE 3 | PAGE 191
Two-dimensional site-bond percolation as an example of self-averaging system
O. A. Vasilyev
L. D. Landau Institute for Theoretical Physics RAS, 117940 Moscow, Russia

PACS: 64.60.Cn, 75.10.Hk
Abstract
The Harris-Aharony for statical model criteria predicts, that if specific heat exponent \alpha \ge 0, then this model does not exhibit self-averaging. In two-dimensional percolation model the index \alpha=-\frac{1}{2}. It means, that in accordance with Harris-Aharony criteria, this model can exhibit self-averaging properties. We study numerically the relative variance RM and Rχ of the probability of site to belong the «infinite" (maximum) cluster M and the mean finite cluster sizes χ. It was shown, that two-dimensional site-bound percolation on the square lattice, where the bonds play role of impurity and sites play role of statistical ensemble, over which the averaging performed, exhibit self-averaging properties.


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