Harmonic measure for critical Potts clusters.
We present a technique, which we call "etching," which we use to study the harmonic measure of Fortuin-Kasteleyn clusters in the Q-state Potts model for Q=1-4 . The harmonic measure is the probability distribution of random walkers diffusing onto the perimeter of a cluster. We use etching to study regions of clusters which are extremely unlikely to be hit by random walkers, having hitting probabilities down to 10-4600. We find good agreement between the theoretical predictions of Duplantier and our numerical results for the generalized dimension D(q) including regions of small and negative q .
Adams
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DA
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA.
Lin
Yen Ting
YT
Sander
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Ziff
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RM