Diluted Potts model on diamond-type hierarchical lattices

1993 ◽  
Vol 48 (5) ◽  
pp. 3171-3176 ◽  
Author(s):  
You-zhi Wu ◽  
Yung Qin ◽  
Z. R. Yang
Keyword(s):  
Potts Model ◽  
Hierarchical Lattices ◽  
Diamond Type

Family of diamond-type hierarchical lattices

1988 ◽  
Vol 38 (1) ◽  
pp. 728-731 ◽  
Author(s):  
Z. R. Yang
Keyword(s):  
Hierarchical Lattices ◽  
Diamond Type

Feigenbaum Julia sets of singularities of free energy

2009 ◽  
Vol 30 (5) ◽  
pp. 1573-1591 ◽  
Author(s):  
JIANYONG QIAO ◽  
YONGCHENG YIN ◽  
JUNYANG GAO
Keyword(s):  
Free Energy ◽  
Potts Model ◽  
Julia Set ◽  
Julia Sets ◽  
Hierarchical Lattices

AbstractConsidering the Potts model on diamond-like hierarchical lattices, in this paper, we show that the Julia sets of the singularities of the free energy may be a Feigenbaum Julia set. Furthermore, we prove that these Julia sets are locally connected if they are connected.

Diamond-type hierarchical lattices for the Potts antiferromagnet

1991 ◽  
Vol 43 (10) ◽  
pp. 8576-8582 ◽  
Author(s):  
Yung Qin ◽  
Z. R. Yang
Keyword(s):  
Hierarchical Lattices ◽  
Diamond Type

scholarly journals Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Weihua Sun ◽  
Shutang Liu
Keyword(s):  
Complex Plane ◽  
Potts Model ◽  
Julia Set ◽  
Nonlinear Coupling ◽  
Rational System ◽  
Fractional Model ◽  
Dynamics And Control ◽  
Hierarchical Lattices ◽  
And Control ◽  
Fractional Orders

The fractional Potts model on diamond-like hierarchical lattices is introduced in this manuscript, which is a fractional rational system in the complex plane. Then, the fractal dynamics of this model is discussed from the fractal viewpoint. Julia set of the fractional Potts model is given, and control items of this fractional model are designed to control the Julia set. To associate two different Julia sets of the fractional model with different parameters and fractional orders, nonlinear coupling items are taken to make one Julia set change to another. The simulations are provided to illustrate the efficacy of these methods.

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