Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/71425
DC Field | Value | Language |
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dc.contributor | 應數系 | en_US |
dc.creator | 張書銓 | zh_TW |
dc.creator | Chang, Shu-Chiuan | en_US |
dc.creator | 陳隆奇 | zh_TW |
dc.creator | Chen, Lung-Chi | en_US |
dc.creator | 李欣芸 | zh_TW |
dc.creator | Lee, Hsin-Yun | en_US |
dc.date | 2013.10 | en_US |
dc.date.accessioned | 2014-11-13T09:26:16Z | - |
dc.date.available | 2014-11-13T09:26:16Z | - |
dc.date.issued | 2014-11-13T09:26:16Z | - |
dc.identifier.uri | http://nccur.lib.nccu.edu.tw/handle/140.119/71425 | - |
dc.description.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. | en_US |
dc.format.extent | 577308 bytes | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | en_US | - |
dc.relation | Physica A, 392(8), 1776-1787 | en_US |
dc.subject | Ice model;Eight-vertex model;Sierpinski gasket;Recursion relations;Entropy | en_US |
dc.title | Ice model and eight-vertex model on the two-dimensional Sierpinski gasket | en_US |
dc.type | article | en |
dc.identifier.doi | 10.1016/j.physa.2013.01.005 | - |
dc.doi.uri | http://dx.doi.org/10.1016/j.physa.2013.01.005 | - |
item.cerifentitytype | Publications | - |
item.fulltext | With Fulltext | - |
item.grantfulltext | restricted | - |
item.languageiso639-1 | en_US | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | article | - |
Appears in Collections: | 期刊論文 |
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1776-1787.pdf | 563.78 kB | Adobe PDF2 | View/Open |
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