Julia sets, Hausdorff dimension and phase transition☆
Julia sets, Hausdorff dimension and phase transition☆
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DOI：
10.1016/j.chaos.2011.07.013
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发表时间：
2011-10
影响因子：
7.8
通讯作者：
Junyang Gao
中科院分区：
文献类型：
--
作者：
Junyang Gao
研究了类钻石等级格上Potts模型配分函数零点的极限集。证明了一类有理映射的极限集是其Julia集，并以数学上精确的方法证明了当参数λ_∞ →+∞时，Julia集趋向于一个几何圆，其Hausdorff维数趋向于1，从而给出了1989年Bambi Hu和Bin Lin提出的一个正确答案，并给出了这一关系的一个完整的描述.并讨论了该物理模型Aλ（1）的能级直径关于λ的连续性。
The limit set of zeros of partition function of the Potts model on diamond-like hierarchical lattices is studied. It is shown that the limit set is the Julia set of a family rational maps, it is shown in a mathematically exact way that the Julia set tends to a geometrical circle and its Hausdorff dimension tends to 1 when the parameter ∣λ∣→+∞, which gives a true answer that Bambi Hu and Bin Lin proposed in 1989, furthermore, in this paper, it give a perfect description about this relations. Also the continuity of level diameter of Aλ(1) of this physical model about λ is discussed.