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 consi...
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| Online Access: | http://irep.iium.edu.my/29714/ http://irep.iium.edu.my/29714/ http://irep.iium.edu.my/29714/ http://irep.iium.edu.my/29714/1/mfom-EPL%282013%29.pdf |
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iium-297142013-04-23T04:30:17Z http://irep.iium.edu.my/29714/ Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models Ostilli, Massimo Mukhamedov, Farrukh QC Physics 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. IOP Publishing 2013-03 Article PeerReviewed application/pdf en http://irep.iium.edu.my/29714/1/mfom-EPL%282013%29.pdf 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) http://iopscience.iop.org/0295-5075/101/6/60008 10.1209/0295-5075/101/60008 |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
| collection |
Online Access |
| language |
English |
| topic |
QC Physics |
| spellingShingle |
QC Physics Ostilli, Massimo Mukhamedov, Farrukh Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models |
| description |
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. |
| format |
Article |
| author |
Ostilli, Massimo Mukhamedov, Farrukh |
| author_facet |
Ostilli, Massimo Mukhamedov, Farrukh |
| author_sort |
Ostilli, Massimo |
| title |
Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models |
| title_short |
Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models |
| title_full |
Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models |
| title_fullStr |
Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models |
| title_full_unstemmed |
Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models |
| title_sort |
continuous- and discrete-time glauber dynamics. first- and second-order phase transitions in mean-field potts models |
| publisher |
IOP Publishing |
| publishDate |
2013 |
| url |
http://irep.iium.edu.my/29714/ http://irep.iium.edu.my/29714/ http://irep.iium.edu.my/29714/ http://irep.iium.edu.my/29714/1/mfom-EPL%282013%29.pdf |
| first_indexed |
2023-09-18T20:43:40Z |
| last_indexed |
2023-09-18T20:43:40Z |
| _version_ |
1777409531686420480 |