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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2013
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| Subjects: | |
| 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 |
| 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. |
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