Site and bond directed branched polymers for arbitrary dimensionality: evidence supporting a relation with the Lee-Yang edge singularity

Parisi and Sourlas (1981) have argued that the isotropic branched polymer problem in dimension d+1 is related to the Lee-Yang edge singularity problem in dimension d-1. To test if there is a relation with the directed branched polymer problem, the authors calculate the generating functions for both site and bond directed branched polymers for arbitrary dimension d to order smax=10 and bmax=8. Their analysis lends support to the proposal that theta (d+1)-1= theta D(d)= sigma LY(d-1)+1, where theta and theta D are the critical exponents for lattice animals and directed lattice animals, and sigma LY is the Lee-Yang edge singularity exponent. They also obtain expansions for the growth parameter in the variable sigma -1=(2d-1)-1 for bond and site directed lattice animals.