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

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Abstract

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.

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Acknowledgements

The authors wish to thank Paolo Dai Pra for having suggested the idea of this work and for all the useful discussions on it and Marco Formentin for the suggestions and comments. This work was partially supported by the INdAM-GNAMPA Project 2017 “Collective periodic behavior in interacting particle systems”. L. A. acknowledges the partial support by Centro Studi Levi Cases (Università di Padova).

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Funding were provided by Università degli Studi di Padova and Weierstrass Institute.

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Authors and Affiliations

  1. WIAS-Weierstrass Institute, Mohrenstr. 39, 10117, Berlin, Germany

    Luisa Andreis

  2. Dipartimento di Matematica “T. Levi-Civita”, Universitá di Padova, via Trieste 63, 35121, Padova, Italy

    Daniele Tovazzi

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  1. Luisa Andreis
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  2. Daniele Tovazzi
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Correspondence to Luisa Andreis.

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Andreis, L., Tovazzi, D. Coexistence of Stable Limit Cycles in a Generalized Curie–Weiss Model with Dissipation. J Stat Phys 173, 163–181 (2018). https://doi.org/10.1007/s10955-018-2127-5

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  • DOI: https://doi.org/10.1007/s10955-018-2127-5

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