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Julia sets, Hausdorff dimension and phase transition

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  • Gao, Junyang

Abstract

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.

Suggested Citation

  • Gao, Junyang, 2011. "Julia sets, Hausdorff dimension and phase transition," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 871-877.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:10:p:871-877
    DOI: 10.1016/j.chaos.2011.07.013
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