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

Abstract

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 ${p}_{c}=0.741\ifmmode\pm\else\textpm\fi{}0.002$ and the exponent for the correlation length $\frac{1}{\ensuremath{\nu}}=0.75\ifmmode\pm\else\textpm\fi{}0.02$, indicating that the model may be in the same universality class as the site percolation problem.