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.

中文翻译：

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Lyapunov指数和相变的临界指数—广义哈密顿平均场模型

我们计算具有远距离相互作用的多粒子系统中最大Lyapunov指数的半解析和数值估计，扩展了具有余弦势的哈密顿平均场模型的先前结果。我们的结果证明了与最大Lyapunov指数幂律衰减相关的临界指数接近二阶相变，接近于余弦哈密顿平均场模型的相同值，表明该指数可能具有普遍性。我们还表明，一阶相变的指数与理论估计值和数值估计值都有不同的值。