The Harmonic Measure for critical Potts clusters

Details The Harmonic Measure for critical Potts clusters The Harmonic Measure for critical Potts clusters

2009-07-14

arxiv.org/abs/0907.2349v2

Phys. Rev. E 80, 031141 (2009)

Physics

Condensed Matter

Statistical Mechanics

20 pages, 10 figures

Scientific paper

10.1103/PhysRevE.80.031141

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.

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