Large scale properties of the IIIC for 2D percolation

L. Chayes and P. Nolin

Stochastic Processes and their Applications, 2009, vol. 119, issue 3, 882-896

Abstract: We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to pc with an inverse power, [lambda], of the distance to the origin. Assuming the existence of critical exponents (as is known in the case of the triangular site lattice) if the power is less than 1/[nu], with [nu] the correlation length exponent, we demonstrate an infinite cluster with scale dimension given by DH=2-[beta][lambda]. Further, we investigate the critical case [lambda]c=1/[nu] and show that iterated logarithmic corrections will tip the balance between the possibility and impossibility of an infinite cluster.

Keywords: Inhomogeneous; percolation; Incipient; infinite; cluster; Critical; exponents (search for similar items in EconPapers)
Date: 2009
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