Percolation by position-space renormalisation group with large cells

Abstract

The authors demonstrate that the critical properties of the percolation model can be obtained with a rather high degree of accuracy by extrapolating to b= infinity a sequence of position-space renormalisation group calculations for finite cells of side b. For b<or=5 we calculate the recursion relations in closed form, while for 4<or=b<or=500 we find the recursion relations by Monte Carlo methods. We then obtain a sequence of estimates for the critical concentration pc and the scaling powers yp and yh at the various values of b. Finally, we introduce a transformation from a cell of side b to a cell of side b', which may be viewed as an 'infinitesimal' transformation with a scale change of b/b'.