Remark on the Dimer Problem
Remark on the Dimer Problem
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DOI：
10.1016/0166-218x(94)90106-6
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发表时间：
1994-06
期刊：
影响因子：
--
通讯作者：
H. Sachs;Holger Zernitz
中科院分区：
文献类型：
--
作者：
H. Sachs;Holger Zernitz
设Sn是2n× 2n正方形格，c（Sn）是Sn的二聚体覆盖数. 1961年，ME Fisher，PW Kasteleyn和HNV Temperley/ME Fisher建立了log c（Sn）与Cs渐近等价的结果，现在已成为经典|S n|其中，Cs> 0是常数。本文考虑了无限正方形格的另一个子集序列{Tn}，它在某种程度上类似于{Sn}，并通过初等方法证明了c（Tn）的渐近性质与c（Sn）的渐近性质完全不同：logc（Tn）<$CT| T n|其中C T> 0是常数。
Let S n be the 2n× 2n square lattice and c (S n) the number of dimer coverings of S n. In 1961, ME Fisher, PW Kasteleyn and HNV Temperley/ME Fisher established the—now classical—result that log c (S n) is asymptotically equivalent to C s| S n| where C s> 0 is a constant. In this paper, another sequence {T n} of subsets of the infinite square lattice is considered which, in a way, is similar to {S n}, and by elementary means it is shown that the asymptotic behaviour of c (T n) is quite different from that of c (S n): in fact, log c (T n)∼ C T| T n| where C T> 0 is a constant.