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Fractal dimensions and corrections to scaling for critical Potts clusters

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arxiv cond-mat/0206367 v2 pith:SSNBW4OC submitted 2002-06-19 cond-mat.stat-mech

A. Aharony , J. Asikainen This is my paper · ORCID
classification cond-mat.stat-mech
keywords correctionsclustersfractalpottsasymptoticbondsconnectedcoulomb
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abstract

Renormalization group and Coulomb gas mappings are used to derive theoretical predictions for the corrections to the exactly known asymptotic fractal masses of the hull, external perimeter, singly connected bonds and total mass of the Fortuin-Kasteleyn clusters for two-dimensional $q$-state Potts models at criticality. For q=4 these include exact logarithmic (as well as loglog) corrections.

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  1. 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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