Critical exponent for the Lyapunov exponent and phase transitions—the generalized Hamiltonian mean-field model

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. (paper)