发帖
雷达卡
摘要翻译：
本文给出了Sierpinski垫片$SG_d(n)$在阶$n$上的二聚体数$N_d(n)$,维数$D$等于2,3,4或5,其中当顶点数$V(n)$为奇数时，最外顶点中的一个不被覆盖。定义为$S_{SG_d}=\lim_{n\to\infty}\ln N_d(n)/v(n)$的双原子分子的每位吸收熵为$\Ln(2)/3$。本文还精确地得到了广义Sierpinski垫片$SG_{d,b}(n)$上的二聚体数，其中$d=2$,$b=3,4,5$。它们的熵分别等于$\ln(6)/7$，$\ln(28)/12$，$\ln(200)/18$。根据$sg_d(n)$在某一阶段的结果，导出了$d=3,4,5$时熵的上界和下界。当这些界限之间的差值随着计算阶段的增加而迅速收敛到零时，$D=3,4,5$的数值$S_{SG_d}$可以精确地计算100多个有效数字。
---
英文标题：
《Dimer coverings on the Sierpinski gasket with possible vacancies on the
outmost vertices》
---
作者：
Shu-Chiuan Chang and Lung-Chi Chen
---
最新提交年份：
2007
---
分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--
---
英文摘要：
We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.
---
PDF链接：
https://arxiv.org/pdf/711.0573
京公网安备 11010802022788号
