Abstract
Temporal evolution toward thermal equilibria is numerically investigated in a Hamiltonian system with many degrees of freedom which exhibits a second order phase transition. Relaxation processes are studied through a local order parameter, and slow relaxations of the power type are observed at the critical energy of the phase transition for some initial conditions. Numerical results are compared with results of a phenomenological theory of statistical mechanics. At the critical energy, the maximum Lyapunov exponent assumes a maximal value. Temporal evolution and probability distributions of local Lyapunov exponents indicate that the system is highly chaotic rather than weakly chaotic at the critical energy. Consequently theories for perturbed systems may not be applicable at the critical energy for the purpose of explaining the slow relaxation of the power type.
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