1/d-expansions for the free energy of weakly embedded site animal models of branched polymers
1/d-expansions for the free energy of weakly embedded site animal models of branched polymers
复制标题
支化聚合物弱嵌入位点动物模型自由能的 1/d 展开
DOI：
--
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
P. J. Peard
中科院分区：
文献类型：
--
作者：
D. S. Gaunt;P. J. Peard
我们给1/d-扩展，为了1/d5，为限制减少自由能的弱嵌入式两个变量网站动物模型的支化聚合物。因此，我们能够推导出相关单变量模型的自由能和弱嵌入树和强嵌入树的生长常数的展开式，再次达到1/d5。我们认为，自由能展开是渐近正确的逸度只有一个小范围内。精确的结果表明，具有紧凑超立方结构的动物对弱嵌入位点动物总数的贡献最大，特别是对于大d。这一结果并没有反映在自由能1/d-扩展，其中树作出了主要贡献。我们还得到新的精确计数数据格动物使用中间计算的1/d-扩展的推导。因此，我们给出了一般d维超立方格1到13个格点的配分函数。
We give the 1/d-expansion, to order 1/d5, 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/d5. 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.