Exact critical exponent for the shortest-path scaling function in percolation
Statistical Mechanics
2009-10-31 v3 Disordered Systems and Neural Networks
Abstract
It is shown that the critical exponent related to pair-connectiveness and shortest-path (or chemical distance) scaling, recently studied by Porto et al., Dokholyan et al., and Grassberger, can be found exactly in 2d by using a crossing-probability result of Cardy, with the outcome . This prediction is consistent with existing simulation results.
Cite
@article{arxiv.cond-mat/9907305,
title = {Exact critical exponent for the shortest-path scaling function in percolation},
author = {Robert M. Ziff},
journal= {arXiv preprint arXiv:cond-mat/9907305},
year = {2009}
}
Comments
References updated, small corrections 4 pages. Published version