Percolation processes in two dimensions. II. Critical concentrations and the mean size index

Abstract

For pt.I see ibid., vol.9, p.87 (1976). New series data are examined for the mean cluster size for site and bond mixtures in two dimensions. The critical concentration for the site problem on the simple quadratic lattice is estimated as p_c=0.593+or-0.002 and on the honeycomb lattice as p_c=0.698+or-0.003. It is concluded that the data are reasonably consistent with the hypothesis that the mean cluster size S(p) approximately=C(p_c-p)^{- gamma} as p to p_c- with gamma a dimensional invariant, gamma =2.43+or-0.03 in two dimensions. Estimates of the critical amplitude C are also given.