Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/71425
題名: | Ice model and eight-vertex model on the two-dimensional Sierpinski gasket | 作者: | 張書銓 Chang, Shu-Chiuan 陳隆奇 Chen, Lung-Chi 李欣芸 Lee, Hsin-Yun |
貢獻者: | 應數系 | 關鍵詞: | Ice model;Eight-vertex model;Sierpinski gasket;Recursion relations;Entropy | 日期: | 2013 | 上傳時間: | 13-Nov-2014 | 摘要: | We present the numbers of ice model configurations (with Boltzmann factors equal to one) I(n)I(n) on the two-dimensional Sierpinski gasket SG(n)SG(n) at stage nn. The upper and lower bounds for the entropy per site, defined as limv→∞lnI(n)/vlimv→∞lnI(n)/v, where vv is the number of vertices on SG(n)SG(n), are derived in terms of the results at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of the entropy can be evaluated with more than a hundred significant figures accuracy. The corresponding result of the ice model on the generalized two-dimensional Sierpinski gasket SGb(n)SGb(n) with b=3b=3 is also obtained, and the general upper and lower bounds for the entropy per site for arbitrary bb are conjectured. We also consider the number of eight-vertex model configurations on SG(n)SG(n) and the number of generalized vertex models Eb(n)Eb(n) on SGb(n)SGb(n), and obtain exactly Eb(n)=2{2(b+1)[b(b+1)/2]n+b+4}/(b+2)Eb(n)=2{2(b+1)[b(b+1)/2]n+b+4}/(b+2). It follows that the entropy per site is View the MathML sourcelimv→∞lnEb(n)/v=2(b+1)b+4ln2. | 關聯: | Physica A, 392(8), 1776-1787 | 資料類型: | article | DOI: | http://dx.doi.org/10.1016/j.physa.2013.01.005 |
Appears in Collections: | 期刊論文 |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
1776-1787.pdf | 563.78 kB | Adobe PDF2 | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.