Evidence for classical critical behavior in long-range site percolation

Abstract

A new large-cell Monte Carlo renormalization group following the approach of Reynolds et al. is developed to study site percolation with long-range interaction. The results show that site percolation with a long, but finite, range of interactions has the same correlation-length exponent ${\ensuremath{\nu}}_{P}$ as ordinary percolation. However, as the interaction range tends to infinity, ${\ensuremath{\nu}}_{P}$ approaches its mean-field value of $\frac{1}{2}$ indicating that infinite-range percolation exhibits classical critical behavior.