Harmonic Measure for Percolation and Ising Clusters Including Rare Events
Statistical Mechanics
2009-11-13 v1
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.
Cite
@article{arxiv.0806.2123,
title = {Harmonic Measure for Percolation and Ising Clusters Including Rare Events},
author = {David A. Adams and Leonard M. Sander and Robert M. Ziff},
journal= {arXiv preprint arXiv:0806.2123},
year = {2009}
}
Comments
4 pages, 5 figures