From discrete to continuous percolation in dimensions 3 to 7
Abstract
We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its continuous limit is controlled by a power-law dependency with a universal exponent θ =3/2 . This allows us to estimate the continuous percolation thresholds in a model of aligned hypercubes in dimensions d=3,\ldots,7 with accuracy far better than that attained using any other method before. We also report improved values of the correlation length critical exponent ν in dimensions d = 4,5 and the values of several universal wrapping probabilities for d=4,\ldots,7 .
- Publication:
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Journal of Statistical Mechanics: Theory and Experiment
- Pub Date:
- October 2016
- DOI:
- 10.1088/1742-5468/2016/10/103206
- arXiv:
- arXiv:1606.08050
- Bibcode:
- 2016JSMTE..10.3206K
- Keywords:
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- Condensed Matter - Statistical Mechanics
- E-Print:
- Journal of Statistical Mechanics: Theory and Experiment, 2016, 103206 (2016)