Lattice trees with specified topologies
Lattice trees with specified topologies
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具有指定拓扑的格子树
DOI：
10.1088/0305-4470/17/1/022
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
M. K. Wilkinson
中科院分区：
文献类型：
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作者：
D. S. Gaunt;J. Lipson;J. Martin;M. Sykes;G. Torrie;S. Whittington;M. K. Wilkinson
研究了具有特定拓扑的格树的总数。对于具有i次ni分支点的强可嵌入(或站点)团簇，它们展示了如何严格地证明增长常数存在且都等于邻域回避行走极限nu。他们得到了与“星型”、“梳型”和“刷型”拓扑相关的临界指数的精确上界。导出并分析了正方形、三角形、简立方和d=4简超立方晶格上某些恒星、梳子和刷子的弱嵌入和强嵌入的精确计数数据。利用一般d维简单超立方晶格的精确计数数据和Bethe晶格内部的精确结果，导出了生长常数的维反指数展开式。这些结果与生长常数等于适当的行走极限(Mu或Nu)是一致的。
The authors study the total numbers of lattice trees with specified topologies. For strongly embeddable (or site) clusters with ni branching points of degree i, they show how to prove rigorously that the growth constants exist and are all equal to the neighbour-avoiding walk limit nu . They derive some exact upper bounds for the critical exponents associated with the 'star', 'comb' and 'brush' topologies. Exact enumeration data are derived and analysed for both weak and strong embeddings of some stars, combs and brushes on the square, triangular, simple cubic and d=4 simple hypercubic lattices. Using the exact enumeration data for the general d-dimensional simple hypercubic lattice and the exact results for the interior of a Bethe lattice, they derive expansions for the growth constants in inverse powers of the dimensionality. These results are consistent with the growth constants being equal to the appropriate walk limits ( mu or nu ).