Harmonic measure for percolation and ising clusters including rare events.
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 percolation. For the complete hull, we find the probability decays with an exponent of -1 for both systems.
Adams
David A
DA
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA.
Sander
Leonard M
LM
Ziff
Robert M
RM