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 $p_c=0.741\mathrm{}\pm 0.002$ and the exponent for the correlation length $\frac{1}{\nu }=0.75\mathrm{}\pm 0.02$, indicating that the model may be in the same universality class as the site percolation problem.

• Received 14 March 1986

DOI:https://doi.org/10.1103/PhysRevB.34.1977