Site and bond directed branched polymers for arbitrary dimensionality: evidence supporting a relation with the Lee-Yang edge singularity
Harry Eugene Stanley, S. Redner, Z R Yang · Journal of Physics A Mathematical and General · 1982
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 s max =10 and b max =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.