ON CORRECTION TO SCALING FOR 2-DIMENSIONAL AND 3-DIMENSIONAL SCALAR AND VECTOR PERCOLATION

A reanalysis of the resistance R of two-and three-dimensional superconducting networks at the percolation threshold p(c), together with the previous results for the elastic moduli K of such networks, shows that there is a unified description of finite-size scaling for scalar and vector transport properties of percolation systems. For a network of linear size L at p(c), and for both scalar and vector percolation in both two and three dimensions, K and R scale with L as L(-x)[a1 + a2(ln L)-1 + a3L-1], where x is the ratio of the associated critical exponent of K or R and the correlation length exponent v of percolation. Although our estimates of x for the resistance of percolation networks are consistent with the previous results, they do indicate that in both two and three dimensions and for both scalar and vector percolation, the leading nonanalytic correction-to-scaling exponent is zero. From a reanalysis of data on diffusion on percolation clusters at p(c), we propose that such correction-to-scaling terms are a general property of dynamics of percolation clusters. We also suggest that for two-dimensional percolation the conductivity exponent t and the super-conductivity exponent s are given by s = t = v - beta/4 = 187/144 = 1.2986..., and the elasticity exponent f is given by f = t + 2v = 571/144 = 3.9652..., where beta is the exponent of the strength of the infinite percolation cluster.