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arXiv · 0806.2123

Harmonic Measure for Percolation and Ising Clusters Including Rare Events

David A. Adams·Leonard M. Sander·Robert M. Ziff
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Abstract

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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David A. Adams, Leonard M. Sander, Robert M. Ziff. 2008-06-12. Harmonic Measure for Percolation and Ising Clusters Including Rare Events. https://doi.org/10.1103/physrevlett.101.144102

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