Correlated percolation and the correlated resistor network

Details Correlated percolation and the correlated resistor network Correlated percolation and the correlated resistor network

1996-10-10

arxiv.org/abs/cond-mat/9610088v1

J. Phys. A: Math. Gen. 30 (1997) 1791

Physics

Condensed Matter

Statistical Mechanics

16 pages, REVTeX, 6 figures included

Scientific paper

10.1088/0305-4470/30/6/007

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.

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