Abstract
This paper is a study of the percolation problem with long-range correlations in the site or bond occupations. An extension of the Harris criterion for the relevance of the correlations is derived for the case that the correlations decay as for large distances .. For the correlations are relevant if (where is the percolation correlation-length exponent), while for the correlations are relevant if .. Applying this criterion to the behavior that results when the correlations are relevant, we argue that the new behavior will have .. It is shown that the correlated bond percolation problem is equivalent to a -state Potts model with quenched disorder in the limit .. With the use of this result, a renormalization-group study of the problem is presented, expanding in and in .. In addition to the normal percolation fixed point, we find a new long-range fixed point. The crossover to this new fixed point follows the extended Harris criterion, and the fixed point has exponents (as predicted) and . Finally, several results on the percolation properties of the Ising model at its critical point are shown to be in agreement with the predictions of this paper.
- Received 15 August 1983
DOI:https://doi.org/10.1103/PhysRevB.29.387
©1984 American Physical Society