| dc.contributor | 應數系 | en_US |
| dc.creator (作者) | 張書銓 | zh_TW |
| dc.creator (作者) | Chang, Shu-Chiuan | en_US |
| dc.creator (作者) | 陳隆奇 | zh_TW |
| dc.creator (作者) | Chen, Lung-Chi | en_US |
| dc.creator (作者) | 李欣芸 | zh_TW |
| dc.creator (作者) | Lee, Hsin-Yun | en_US |
| dc.date (日期) | 2013.10 | en_US |
| dc.date.accessioned | 13-Nov-2014 17:26:16 (UTC+8) | - |
| dc.date.available | 13-Nov-2014 17:26:16 (UTC+8) | - |
| dc.date.issued (上傳時間) | 13-Nov-2014 17:26:16 (UTC+8) | - |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/71425 | - |
| dc.description.abstract (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. | en_US |
| dc.format.extent | 577308 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.language.iso | en_US | - |
| dc.relation (關聯) | Physica A, 392(8), 1776-1787 | en_US |
| dc.subject (關鍵詞) | Ice model;Eight-vertex model;Sierpinski gasket;Recursion relations;Entropy | en_US |
| dc.title (題名) | Ice model and eight-vertex model on the two-dimensional Sierpinski gasket | en_US |
| dc.type (資料類型) | article | en |
| dc.identifier.doi (DOI) | 10.1016/j.physa.2013.01.005 | - |
| dc.doi.uri (DOI) | http://dx.doi.org/10.1016/j.physa.2013.01.005 | - |
