Abstract
Shows that the generalised lattice animal model of Family and Coniglio (1980) naturally leads to a unified scaling picture for percolation and lattice animals in which the fugacity for occupied elements plays the dual role of a temperature-like and a field-like variable. Within this single-scaling-field description of percolation, there is only one independent exponent from which all others can be obtained. The author defines a new set of exponents alpha , beta and gamma for percolation and finds that they are all related to the cluster number exponent theta through the relation alpha = gamma =1- beta =3- theta , in analogy with lattice animals. To relate the cluster radius exponent nu to the other exponents he uses the generalised Ginzburg criteria to obtain a modified hyperscaling relation for isotropic and directed, percolation and lattice animals. Using this relation he finds that theta -1= nu /sub ///+perpendicular to (d-1) for directed percolation and theta = nu perpendicular to (d-1) for directed lattice animals where nu /sub /// and nu perpendicular to are exponents characterising the parallel and perpendicular cluster radii respectively. Using the same approach he obtains the Stauffer relation theta -1=d nu and the Parisi-Sourlas relation theta -1=(d-2) nu for isotropic percolation and lattice animals respectively. The above relations give the following expressions for theta within the Flory theory: theta (percolation)=(3d+2)/(d+2), theta (directed percolation)=(6d+5)/(2d+4), theta (animals)=(7d-6)/(2d+4) and theta (directed animals)=9(d-1)/(4d+8).