Abstract
Box counting fractal dimensions of Julia sets of the Q-state ferromagnetic Potts model on Bethe lattices are studied. It is shown that Julia sets are circles centered at the origin for values of magnetic field corresponding to the Yang-Lee zeros of the partition function. Also, for values of magnetic field from the Mandelbrot-like set on the complex magnetic field plane Julia sets are simply connected closed Jordan curves and for values of magnetic field outside the Mandelbrot-like set the Julia set is a Cantor set. Moreover, it is shown that the fractal dimension of a Julia set for a value of magnetic field corresponding to a Yang-Lee zero of the partition function is a local minimum as a function of magnetic field.
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Ghulghazaryan, R., Ananikyan, N., Jonassen, T.M. (2003). Julia Sets and Yang-Lee Zeros of the Potts Model on Bethe Lattices. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Dongarra, J.J., Zomaya, A.Y., Gorbachev, Y.E. (eds) Computational Science — ICCS 2003. ICCS 2003. Lecture Notes in Computer Science, vol 2657. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44860-8_9
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