Coexistence of Stable Limit Cycles in a Generalized Curie–Weiss Model with Dissipation

Journal Article · Mon Oct 15 00:00:00 EDT 2018 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/S10955-018-2127-5· OSTI ID:22783689

Andreis, Luisa ^[1]; Tovazzi, Daniele ^[2]

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1. WIAS-Weierstrass Institute (Germany)
2. Universitá di Padova, Dipartimento di Matematica “T. Levi-Civita” (Italy)

In this paper, we modify the Langevin dynamics associated to the generalized Curie–Weiss model by introducing noisy and dissipative evolution in the interaction potential. We show that, when a zero-mean Gaussian is taken as single-site distribution, the dynamics in the thermodynamic limit can be described by a finite set of ODEs. Depending on the form of the interaction function, the system can have several phase transitions at different critical temperatures. Because of the dissipation effect, not only the magnetization of the systems displays a self-sustained periodic behavior at sufficiently low temperature, but, in certain regimes, any (finite) number of stable limit cycles can exist. We explore some of these peculiarities with explicit examples.

• OSTI ID: 22783689
• Journal Information: Journal of Statistical Physics, Vol. 173, Issue 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CRITICAL TEMPERATURE
CURIE-WEISS LAW
DIFFUSION
DISTRIBUTION
INTERACTIONS
LIMIT CYCLE
MAGNETIZATION
MEAN-FIELD THEORY
PERIODICITY
PHASE TRANSFORMATIONS
SIMULATION
THERMODYNAMICS