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 JAMP  Vol.8 No.6 , June 2020
Comparison of Ising Model and Potts Model on Non-Local Directed Small-World Networks
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.
Cite this paper: Sumour, M. , Srour, M. , Baraka, S. , Radwan, M. , Khozondar, R. and Shabat, M. (2020) Comparison of Ising Model and Potts Model on Non-Local Directed Small-World Networks. Journal of Applied Mathematics and Physics, 8, 1031-1038. doi: 10.4236/jamp.2020.86080.
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