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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 2013.10
上傳時間 13-Nov-2014 17:26:16 (UTC+8)
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
dc.contributor 應數系en_US
dc.creator (作者) 張書銓zh_TW
dc.creator (作者) Chang, Shu-Chiuanen_US
dc.creator (作者) 陳隆奇zh_TW
dc.creator (作者) Chen, Lung-Chien_US
dc.creator (作者) 李欣芸zh_TW
dc.creator (作者) Lee, Hsin-Yunen_US
dc.date (日期) 2013.10en_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), 1776-1787en_US
dc.subject (關鍵詞) Ice model;Eight-vertex model;Sierpinski gasket;Recursion relations;Entropyen_US
dc.title (題名) Ice model and eight-vertex model on the two-dimensional Sierpinski gasketen_US
dc.type (資料類型) articleen
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-