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    题名: Dimers on a simple-quartic net with a vacancy
    作者: 曾文哲;Tzeng, Wen-jer;Wu, F. Y.
    贡献者: 淡江大學物理學系
    关键词: Dimersspanning;treesfinite-size;analysis
    日期: 2003-03
    上传时间: 2009-12-31 10:31:22 (UTC+8)
    出版者: Springer
    摘要: A seminal milestone in lattice statistics is the exact solution of the enumeration of dimers on a simple-quartic net obtained by Fisher, Kasteleyn, and Temperley (FKT) in 1961. An outstanding related and yet unsolved problem is the enumeration of dimers on a net with vacant sites. Here we consider this vacant-site problem with a single vacancy occurring at certain specific sites on the boundary of a simple-quartic net. First, using a bijection between dimer and spanning tree configurations due to Temperley, Kenyon, Propp, and Wilson, we establish that the dimer generating function is independent of the location of the vacancy, and deduce a closed-form expression for the generating function. We next carry out finite-size analyses of this solution as well as that of the FKT solution. Our analyses lead to a logarithmic correction term in the large-size expansion for the vacancy problem with free boundary conditions. A concrete example exhibiting this difference is given. We also find the central charge c=−2 in the language of conformal field theory for the vacancy problem, as versus the value c=1 when there is no vacancy.
    關聯: Journal of Statistical Physics 110(3-6), pp.671-689
    DOI: 10.1023/A:1022155701655
    显示于类别:[物理學系暨研究所] 期刊論文


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