1 D-EXPANSIONS FOR THE FREE-ENERGY OF LATTICE ANIMAL-MODELS OF A SELF-INTERACTING BRANCHED POLYMER/

We model a self-interacting branched polymer by a nearest-neighbour co ntact model of lattice animals with either site or bond counting (k- a nd k'-models, respectively). 1/d-expansions for the reduced limiting f ree energy are derived through order 1/d(5) in which the coefficients are temperature dependent. By evaluating the coefficients at certain s pecial temperatures, we obtain 1/d-expansions for the growth constants of various types of lattice animal, again through order 1/d(5). The 1 /d-expansions are used to obtain numerical estimates of the growth con stants and to study the temperature dependence of the reduced limiting free enegies on d-dimensional simple hypercubic lattices for values o f 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.