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Science in China Series A: Mathematics

, Volume 48, Issue 3, pp 388–412 | Cite as

Julia sets and complex singularities in diamond-like hierarchical Potts models

  • Jianyong Qiao
Article

Abstract

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.

Keywords

Julia set phase transition iteration, rational mapping 

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Copyright information

© Science in China Press 2005

Authors and Affiliations

  1. 1.Center of MathematicsChina University of Mining & TechnologyBeijingChina

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