Julia sets and Yang-Lee zeros of the Potts model on bethe lattices

  • Authors:

  • Ruben Ghulghazaryan;Nerses Ananikyan;Tore M. Jonassen

  • Affiliations:

  • Department of Theoretical Physics, Yerevan Physics Institute, Yerevan, Armenia;Department of Theoretical Physics, Yerevan Physics Institute, Yerevan, Armenia and Institute of Physics, Academia Sinica, Taipei, Taiwan;Department of Computer Science, Oslo University College, Oslo, Norway

  • Venue:
  • ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
  • Year:
  • 2003

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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 magnetics 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 magnetics field outsides 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 alocal minimum as a function of magnetic field.