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

Ostilli, Massimo and Mukhamedov, Farrukh (2013) Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models. EPL (Europhysics Letters), 101 (6). 60008-p1. ISSN 1286-4854 (O), 0295-5075 (P)

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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 � 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.

Item Type:	Article (Journal)
Additional Information:	5537/29714
Uncontrolled Keywords:	Condensed matter: structural, mechanical & thermal Statistical physics and nonlinear systems
Subjects:	Q Science > QC Physics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	23 Apr 2013 12:30
Last Modified:	23 Apr 2013 12:30
URI:	http://irep.iium.edu.my/id/eprint/29714

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