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arXiv · 1912.02506

Critical Exponent for the Lyapunov Exponent and Phase Transitions -- The Generalized Hamiltonian Mean-Field Model

Moisés F. P. Silva Jr·Tarcísio M. Rocha Filho·Yves Elskens
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Abstract

We compute semi-analytic and numerical estimates for the largest Lyapunov exponent in a many-particle system with long-range interactions, extending previous results for the Hamiltonian Mean Field model with a cosine potential. Our results evidence a critical exponent associated to a power law decay of the largest Lyapunov exponent close to second-order phase-transitions, close to the same value as for the cosine Hamiltonian Mean Field model, suggesting the possible universality of this exponent. We also show that the exponent for first-order phase transitions has a different value from both theoretical and numerical estimates.

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Moisés F. P. Silva Jr, Tarcísio M. Rocha Filho, Yves Elskens. 2019-12-05. Critical Exponent for the Lyapunov Exponent and Phase Transitions -- The Generalized Hamiltonian Mean-Field Model. https://doi.org/10.1088/1751-8121/ab876d

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