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

• Main Authors: Ostilli, Massimo, Mukhamedov, Farrukh
• Format: Article
• Language: English
• Published: IOP Publishing 2013
• Subjects: QC Physics
• Online Access: http://irep.iium.edu.my/29714/1/mfom-EPL%282013%29.pdf; http://irep.iium.edu.my/29714/; http://iopscience.iop.org/0295-5075/101/6/60008

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 � 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.