Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models

M. Ostilli; F. Mukhamedov

doi:10.1209/0295-5075/101/60008

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arXiv · 1304.0814

Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models

M. Ostilli·F. Mukhamedov

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Abstract

As is known, at the Gibbs-Boltzmann equilibrium, the mean-field $q$-state Potts model with a ferromagnetic coupling has only a first order phase transition when $q\geq 3$, while there is no phase transition for an antiferromagnetic coupling. The same equilibrium is asymptotically reached when one considers the continuous time evolution according to a Glauber dynamics. In this paper we show that, when we consider instead the Potts model evolving according to a discrete-time dynamics, the Gibbs-Boltzmann equilibrium is reached only when the coupling is ferromagnetic while, when the coupling is anti-ferromagnetic, a period-2 orbit equilibrium is reached and a stable second-order phase transition in the Ising mean-field universality class sets in for each component of the orbit. We discuss the implications of this scenario in real-world problems.

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M. Ostilli, F. Mukhamedov. 2013-04-02. Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models. https://doi.org/10.1209/0295-5075%2F101%2F60008

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