Monte Carlo renormalisation group approach to critical percolation behaviour in three dimensions: simple cubic lattice

Abstract

A Monte Carlo renormalisation group approach using a scaling transformation in real space is applied to the critical properties for the site percolation problem on the simple cubic lattice. The authors find a sequence of estimates for the critical concentration pc and the eigenvalue lambda at various values of the rescaling length b. Extrapolation of these sequences to the limit b to infinity yields the site percolation threshold pc=0.3115+0.0004/-0.0003 and the connectedness length exponent nu =0.88+or-0.04.