Universality of Finite-Size Corrections to the Number of Critical Percolation Clusters
1997; American Physical Society; Volume: 79; Issue: 18 Linguagem: Inglês
10.1103/physrevlett.79.3447
ISSN1092-0145
AutoresRobert M. Ziff, Steven R. Finch, Victor Adamchik,
Tópico(s)Complex Network Analysis Techniques
ResumoMonte Carlo simulations on a variety of finite 2D percolating systems at criticality suggest that the excess number of clusters over the bulk value ${n}_{c}$ is a universal quantity, dependent upon the system shape but independent of the lattice and percolation type. Values of ${n}_{c}$ are found to high accuracy, and for bond percolation are in accord with the theoretical predictions of Temperley and Lieb [Proc. R. Soc. London A 322, 251 (1971)], and Baxter, Temperley, and Ashley [Proc. R. Soc. London A 358, 535 (1978)], whose results we have evaluated explicitly in terms of simple algebraic numbers. Fluctuations are also studied.
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