Correlated percolation and the correlated resistor network
Statistical Mechanics
2009-10-28 v1
Abstract
We present some exact results on percolation properties of the Ising model, when the range of the percolating bonds is larger than nearest-neighbors. We show that for a percolation range to next-nearest neighbors the percolation threshold Tp is still equal to the Ising critical temperature Tc, and present the phase diagram for this type of percolation. In addition, we present Monte Carlo calculations of the finite size behavior of the correlated resistor network defined on the Ising model. The thermal exponent t of the conductivity that follows from it is found to be t = 0.2000 +- 0.0007. We observe no corrections to scaling in its finite size behavior.
Keywords
Cite
@article{arxiv.cond-mat/9610088,
title = {Correlated percolation and the correlated resistor network},
author = {Paul J. M. Bastiaansen and Hubert J. F. Knops},
journal= {arXiv preprint arXiv:cond-mat/9610088},
year = {2009}
}
Comments
16 pages, REVTeX, 6 figures included