Summary: UM­ChE­96/004
Universality of finite­size corrections to the number of critical
percolation clusters
Robert M. Ziff, 1 Steven R. Finch, 2 and Victor S. Adamchik 3
1 University of Michigan, Ann Arbor, MI 48109­2136
2 MathSoft, Inc., Cambridge, MA 02142­1521
3 Wolfram Research, Inc., Champaign, IL 61820­7237
(August 28, 1997)
Abstract
Monte­Carlo simulations on a variety of 2d percolating systems at crit­
icality suggest that the excess number of clusters in finite systems 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 confirm the theoretical predictions
of Temperley and Lieb, and Baxter, Temperley and Ashley, which we have
evaluated explicitly in terms of simple algebraic numbers. Predictions for the
fluctuations are confirmed numerically for the first time.
PACS numbers(s): 64.60Ak, 05.70.Jk
Typeset using REVT E X
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Source: Adamchik, Victor - School of Computer Science, Carnegie Mellon University

Collections: Computer Technologies and Information Sciences