Monte Carlo renormalisation-group approach to percolation on a continuum: test of universality

Abstract

It is shown that a Monte Carlo renormalisation-group technique can be employed for direct renormalisation of a system on a continuum, i.e. without restriction to a periodic lattice. For the problem of overlapping discs the authors find the critical area fraction s_c=0.688+or-0.005 and the correlation-length critical exponent nu =1.33+or-0.07. The latter result indicates the regular-irregular lattice universality.