Correction-to-scaling exponent for two-dimensional percolation

Robert M. Ziff

Correction-to-scaling exponent for two-dimensional percolation

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arxiv 1101.0807 v1 pith:OZPALZHR submitted 2011-01-04 cond-mat.dis-nn

Robert M. Ziff This is my paper · ORCID

classification cond-mat.dis-nn

keywords percolationomegacorrection-to-scalingmeasurementsresultsitetwo-dimensionalannulus

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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_1 = nu omega <= 2, based upon Cardy's result for the critical 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 presented here, suggesting this result is exact. A scaling form evidently applicable to site percolation is also found.

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Correction-to-scaling exponent for percolation and the Fortuin--Kasteleyn Potts model in two dimensions
cond-mat.stat-mech 2024-11 conditional novelty 5.0 of 10

For two-dimensional Fortuin-Kasteleyn Potts clusters, the correction-to-scaling exponent is predicted exactly as Ω = 8/[(2g+1)(2g+3)] = 1/(g d_f), matching Monte Carlo data for Q=1,2,3,4 on critical and tricritical branches.

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