Abstract
Further to the investigation of the critical properties of the Potts model with q = 3 and 8 states in one dimension (1D) on directed small-world networks reported by Aquino and Lima, which presents, in fact, a second-order phase transition with a new set of critical exponents, in addition to what was reported in Sumour and Lima in studying Ising model on non-local directed small-world for several values of probability 0 < P < 1. In this paper the behavior of two models discussed previously, will be re-examined to study differences between their behavior on directed small-world networks for networks of different values of probability P = 0.1, 0.2, 0.3, 0.4 and 0.5 with different lattice sizes L = 10, 20, 30, 40, and 50 to compare between the important physical variables between Ising and Potts models on the directed small-world networks. We found in our paper that is a phase transitions in both Ising and Potts models depending essentially on the probability P.
Highlights
Networks of coupled dynamics systems have been used to numerically model many self-organizing systems, such as biological oscillators, neural networks, spatial games and genetic control networks [1] and the references therein
Further to the investigation of the critical properties of the Potts model with q = 3 and 8 states in one dimension (1D) on directed small-world networks reported by Aquino and Lima, which presents, a second-order phase transition with a new set of critical exponents, in addition to what was reported in Sumour and Lima in studying Ising model on non-local directed small-world for several values of probability 0 < P < 1
We determined the “flatness” of the curves of Potts and Ising model as (−0.76), and (−2.87) respectively, and we find that Ising and Potts model illustrates a continuous phase transition and the decay behavior of magnetization which agrees with magnetization universality
Summary
Networks of coupled dynamics systems have been used to numerically model many self-organizing systems, such as biological oscillators, neural networks, spatial games and genetic control networks [1] and the references therein. Potts model with q = 3 and 4 states on directed small-world networks (DSWN) as a function of temperature. Ising model on non-local directed small-world lattices has a second-order phase transition with new critical exponents dependent on p (0 < p < 1). Most of all of researches in Ising and Potts models studied the magnetization, susceptibility, fourth-order Binder Cumulant, and energy. All of these parameters were studied as a function of temperature. There parameters are determined and analyzed for both models [4] [8] to study the similarities and differences between them The behavior of these models on the directed small-world networks for networks is covered
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