Slow Relaxation at Critical Point of Second Order Phase Transition in a Highly Chaotic Hamiltonian System

Abstract

Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and slow relaxations of power type are observed at the critical energy of 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 takes the largest value. Temporal evolutions and probability distributions of local Lyapunov exponents show that the system is highly chaotic rather than weakly chaotic at the critical energy. Consequently theories for perturbed systems may not be applied to the system at the critical energy in order to explain the slow relaxation of power type.