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Temporal evolutions toward thermal equilibria are numerically investigated ina Hamiltonian system with many degrees of freedom which has second order phasetransition. Relaxation processes are studied through local order parameter, andslow relaxations of power type are observed at the critical energy of phasetransition for some initial conditions. Numerical results are compared withresults of a phenomenological theory of statistical mechanics. At the criticalenergy, the maximum Lyapunov exponent takes the largest value. Temporalevolutions and probability distributions of local Lyapunov exponents show thatthe system is highly chaotic rather than weakly chaotic at the critical energy.Consequently theories for perturbed systems may not be applied to the system atthe critical energy in order to explain the slow relaxation of power type.Comment: 16 pages, LaTeX, 13 Postscript figure

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