政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/71425

English | 正體中文 | 简体中文 | Post-Print筆數 : 27 | Items with full text/Total items : 113656/144643 (79%)
Visitors : 51719043 Online Users : 644

RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.

Home ‧ Login ‧ Upload ‧ Help ‧ About ‧ Administer

政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 > Item 140.119/71425

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/71425

Title:	Ice model and eight-vertex model on the two-dimensional Sierpinski gasket
Authors:	張書銓 Chang, Shu-Chiuan 陳隆奇 Chen, Lung-Chi 李欣芸 Lee, Hsin-Yun
Contributors:	應數系
Keywords:	Ice model;Eight-vertex model;Sierpinski gasket;Recursion relations;Entropy
Date:	2013.10
Issue Date:	2014-11-13 17:26:16 (UTC+8)
Abstract:	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.
Relation:	Physica A, 392(8), 1776-1787
Data Type:	article
DOI 連結:	http://dx.doi.org/10.1016/j.physa.2013.01.005
DOI:	10.1016/j.physa.2013.01.005
Appears in Collections:	[應用數學系] 期刊論文

Files in This Item:

File	Description	Size	Format
1776-1787.pdf		563Kb	Adobe PDF2	889	View/Open

社群 sharing

著作權政策宣告 Copyright Announcement

1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.

Loading...