Julia sets and complex singularities in diamond-like hierarchical Potts models
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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.
KeywordsJulia set phase transition iteration, rational mapping
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- 5.Erzan, A., Hierarchical q-state Potts models with periodic and aperiodic renormalization group trajectories, Phys. Lett., 1983, A93A: 237–140.Google Scholar