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

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...

Full description

Saved in:
Bibliographic Details
Published in:Europhysics letters 2013-03, Vol.101 (6), p.60008
Main Authors: Ostilli, M., Mukhamedov, F.
Format: Article
Language:English
Subjects:
05.50.+q
64.60.Bd
64.70.-p
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/101/60008