Julia sets and complex singularities in diamond-like hierarchical Potts models
Julia sets and complex singularities in diamond-like hierarchical Potts models
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DOI：
10.1360/04ys0180
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发表时间：
2005-03
影响因子：
1.4
通讯作者：
Qiao Jianyong
中科院分区：
文献类型：
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作者：
Qiao Jianyong
我们研究了类金刚石层次晶格上Potts模型的相变。证明了复奇点的集合是有理映射的Julia集合。一个有趣的问题是这些奇点是如何延续到复平面上的。本文利用复动力学的方法，给出了复奇异点集合的连通性的完整描述。
We study the phase transition of the Potts model on diamond-like hierarchical lattices. It is shown that the set of the complex singularities is the Julia set of a rational mapping. An interesting problem is how are these singularities continued to the complex plane. In this paper, by the method of complex dynamics, we give a complete description about the connectivity of the set of the complex singularities.