Sharpness of the Phase Transition in Percolation Models *

@inproceedings{Aizenman2004SharpnessOT,
title={Sharpness of the Phase Transition in Percolation Models *},
author={Michael Aizenman and David J. Barsky},
year={2004}
}

The equality of two critical points the percolation threshold pH and the point pτ where the cluster size distribution ceases to decay exponentially is proven for all translation invariant independent percolation models on homogeneous d-dimensional lattices (d^ 1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameter M(β, h\ which for h = Q reduces to the percolation density P^ at the bond density p = l—e~ in the single parameter case. These… CONTINUE READING