1/d-expansions for the free energy of lattice animal models of a self-interacting branched polymer

Abstract

We model a self-interacting branched polymer by a nearest-neighbour contact model of lattice animals with either site or bond counting (k- and k'-models, respectively). 1/d-expansions for the reduced limiting free energy are derived through order l/d5 in which the coefficients are temperature dependent. By evaluating the coefficients at certain special temperatures, we obtain 1/d-expansions for the growth constants of various types of lattice animal, again through order 1/dd. The 1/d-expansions are used to obtain numerical estimates of the growth constants and to study the temperature dependence of the reduced limiting free energies on d-dimensional simple hypercubic lattices for values of d up to the upper critical dimension. The results are compared with ones obtained by more conventional series methods. Unexpected results are obtained for a range of values of the temperature variable.