  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.
