Harmonic Measure for Percolation and Ising Clusters Including Rare Events

Details Harmonic Measure for Percolation and Ising Clusters Including Rare Events Harmonic Measure for Percolation and Ising Clusters Including Rare Events

2008-06-12

arxiv.org/abs/0806.2123v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.101.144102

We obtain the harmonic measure of the hulls of critical percolation clusters and Ising-model Fortuin-Kastelyn clusters using a biased random-walk sampling technique which allows us to measure probabilities as small as 10^{-300}. We find the multifractal D(q) spectrum including regions of small and negative q. Our results for external hulls agree with Duplantier's theoretical predictions for D(q) and his exponent -23/24 for the harmonic measure probability distribution. For the complete hull, we find the probability decays with an exponent of -1 for both systems.

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