Julia sets, Hausdorff dimension and phase transition

Junyang Gao

Chaos, Solitons & Fractals, 2011, vol. 44, issue 10, 871-877

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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:44:y:2011:i:10:p:871-877

DOI: 10.1016/j.chaos.2011.07.013

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