Large-cell Monte Carlo renormalization group for a new type of environmental percolation

O. F. de Alcantara Bonfim, University of Portland
M. Engelsberg

Copyright 1986 American Physical Society. The original published version of this article may be found at


As a simple model for some diluted magnetic systems which present high percolation thresholds, we study a new type of environmental percolation model. In this model two neighboring magnetic sites are considered to be in the same cluster only if their nearest-neighbor sites in the same direction of the line joining them are also magnetic. By using a large-cell Monte Carlo renormalization-group method the percolation threshold in a square lattice is found to be pc=0.741±0.002 and the exponent for the correlation length 1ν=0.75±0.02, indicating that the model may be in the same universality class as the site percolation problem.