Comparison of Ising Model and Potts Model on Non-Local Directed Small-World Networks

Sumour, Muneer A. and Srour, Moeen and Baraka, Sulieman and Radwan, Mohammed A. and Khozondar, Rifa and Shabat, Mohammed M. (2020) Comparison of Ising Model and Potts Model on Non-Local Directed Small-World Networks. Journal of Applied Mathematics and Physics, 8. pp. 1031-1038. ISSN 2327-4379

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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

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