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Phase Transitions and Chaos in Long-Range Models of Coupled Oscillators

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arxiv 0807.1870 v4 pith:GVVRT3YD submitted 2008-07-11 cond-mat.stat-mech astro-phnlin.CDnucl-thphysics.class-phphysics.plasm-ph

G. Miritello , A. Pluchino , A. Rapisarda This is my paper · ORCID
classification cond-mat.stat-mechastro-phnlin.CDnucl-thphysics.class-phphysics.plasm-ph
keywords modelphasebehaviorcoupledkuramotomodelstransitionanalogous
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We study the chaotic behavior of the synchronization phase transition in the Kuramoto model. We discuss the relationship with analogous features found in the Hamiltonian Mean Field (HMF) model. Our numerical results support the connection between the two models, which can be considered as limiting cases (dissipative and conservative, respectively) of a more general dynamical system of damped-driven coupled pendula. We also show that, in the Kuramoto model, the shape of the phase transition and the largest Lyapunov exponent behavior are strongly dependent on the distribution of the natural frequencies.

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  1. Probing Thermodynamic Phase Transitions of 4D R-Charged Black Holes via Lyapunov Exponent

    gr-qc 2025-05 conditional novelty 4.0 of 10

    For 4D R-charged black holes, the Lyapunov exponent of unstable circular orbits tracks black hole phase transitions, and its discontinuity near the critical point shows a universal critical exponent of 1/2.

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