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On connectivity of Julia sets of Yang-Lee zeros. (English) Zbl 1135.82307

Summary: We prove that the Julia sets of the Yang-Lee zeros of the Potts model on the diamond hierarchical lattice are connected sets on the complex plane.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
82B26 Phase transitions (general) in equilibrium statistical mechanics
82B28 Renormalization group methods in equilibrium statistical mechanics
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