From dilute to dense self-avoiding walks on hypercubic lattices
From dilute to dense self-avoiding walks on hypercubic lattices
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超立方晶格上从稀到稠的自回避行走
DOI：
10.1007/bf01023861
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发表时间：
1988
影响因子：
1.6
通讯作者：
M. Coutinho
中科院分区：
文献类型：
--
作者：
A. M. Nemirovsky;M. Coutinho
给出了一维周期边界条件下超立方晶格上单次自回避行走的位形数的场论表示。我们评估的连接常数作为一个功能的fractionfof网站所占据的聚合物链。平均场近似在无限维的极限下是精确的，并且可以系统地计算d − 1次方的修正。整个二阶计算的连接常数和位点熵与二维和三维的已知结果相当。我们还发现，每个位点的熵在f 1−（2d）−1处出现最大值。福特=2（d=3）时，这个最大值出现在f ~0.80（f~0.86）处，它的值比哈密顿行走的单位点熵（f=1）大约高50%（30%）。
A field-theoretic representation is presented to count the number of configurations of a single self-avoiding walk on a hypercubic lattice inddimensions with periodic boundary conditions. We evaluate the connectivity constant as a function of the fractionfof sites occupied by the polymer chain. The meanfield approximation is exact in the limit of infinite dimensions, and corrections to it in powers ofd−1can be systematically evaluated. The connectivity constant and the site entropy calculated throughout second order compare well with known results in two and three dimensions. We also find that the entropy per site develops a maximum atf≳1−(2d)−1. Ford=2 (d=3), this maximum occurs atf~0.80 (f~0.86) and its value is about 50% (30%) higher than the entropy per site of a Hamiltonian walk (f=1).