M. Ostilli, F. Mukhamedov
We analyze a three-states Potts model built over a ring, with coupling J_0, and the fully connected graph, with coupling J. This model is an effective mean-field and can be solved exactly by using transfer-matrix method and Cardano formula. When J and J_0 are both positive, the model has a first-order phase transition which turns out to be a smooth modification of the known phase transition of the traditional mean-field Potts model (J>0 and J_0=0), despite the connected correlation functions are now non zero. However, when J is positive and J_0 negative, besides the first-order transition, there appears also a hidden (non stable) continuous transition. Furthermore, if J is negative, even if the model does not own a proper thermodynamic limit, the dynamics induced by the mean-field equations lead to stable orbits of period 2 with a second-order phase transition and with the classical critical exponent \beta=1/2, like in the Ising model.
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http://arxiv.org/abs/1205.6777
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