1/d-expansions for the free energy of weakly embedded site animal models of branched polymers
D S Gaunt; P J Peard; D S Gaunt; Department of Physics, King's College, Strand, London WC2R 2LS, UK; P J Peard; Department of Physics, King's College, Strand, London WC2R 2LS, UK
Журнал:
Journal of Physics A: Mathematical and General
Дата:
2000-10-27
Аннотация:
We give the 1/d-expansion, to order 1/d<sup>5</sup>, for the limiting reduced free energy of a weakly embedded two-variable site animal model of branched polymers. Hence, we are able to derive expansions for the free energy of related one-variable models and the growth constant of weakly and strongly embedded trees, again to order 1/d<sup>5</sup>. We argue that the free energy expansions are asymptotically correct for a small range of fugacities only. Exact results show that animals with a compact hypercubic structure make the overwhelming contribution to the total number of weakly embedded site animals, especially for large d. This result is not reflected in the free energy 1/d-expansions, where trees make the dominant contribution. We also derive new exact enumeration data for lattice animals using intermediate calculations in the derivation of the 1/d-expansions. Thus, we give partition functions for the general d-dimensional hypercubic lattice for one to 13 sites.
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