Mean-field critical behaviour for correlation length for percolation in high dimensions

@article{Hara1990MeanfieldCB,
title={Mean-field critical behaviour for correlation length for percolation in high dimensions},
author={T. Hara},
journal={Probability Theory and Related Fields},
year={1990},
volume={86},
pages={337-385}
}

SummaryExtending the method of [27], we prove that the corrlation length ξ of independent bond percolation models exhibits mean-field type critical behaviour (i.e. ξ(p∼(pc−p)−1/2 asp↗pc) in two situations: i) for nearest-neighbour independent bond percolation models on ad-dimensional hypercubic lattice ℤd, withd sufficiently large, and ii) for a class of “spread-out” independent bond percolation models, which are believed to belong to the same universality class as the nearest-neighbour model… Expand