Correction-to-scaling exponent for two-dimensional percolation

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.83.020107· OSTI ID:21560025

Ziff, Robert M ^[1]

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1. Center for the Study of Complex Systems and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109 (United States)

We show that the correction-to-scaling exponents in two-dimensional percolation are bounded by {Omega}{<=}72/91, {omega}=D{Omega}{<=}3/2, and {Delta}{sub 1}={nu}{omega}{<=}2, based upon Cardy's result for the crossing probability on an annulus. The upper bounds are consistent with many previous measurements of site percolation on square and triangular lattices and new measurements for bond percolation, suggesting that they are exact. They also agree with exponents for hulls proposed recently by Aharony and Asikainen, based upon results of den Nijs. A corrections scaling form evidently applicable to site percolation is also found.

• OSTI ID: 21560025
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 83, Issue 2; Other Information: DOI: 10.1103/PhysRevE.83.020107; (c) 2011 American Institute of Physics; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CORRECTIONS
LATTICE PARAMETERS
PROBABILITY
SCALING
TWO-DIMENSIONAL CALCULATIONS