The Harmonic Measure for critical Potts clusters
Statistical Mechanics
2009-10-07 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0907.2349,
title = {The Harmonic Measure for critical Potts clusters},
author = {David A. Adams and Yen Ting Lin and Leonard M. Sander and Robert M. Ziff},
journal= {arXiv preprint arXiv:0907.2349},
year = {2009}
}
Comments
20 pages, 10 figures