Metastability and weak mixing in classical long-range many-rotator systems.

We perform a molecular dynamical study of the isolated d=1 classical Hamiltonian H=1 / 2 summation operator (N)(i=1)L(2)(i)+ summation operator (i not equal j)[1-cos(theta(i)-theta(j))]/r(alpha)(ij); (alpha> or =0), known to exhibit a second order phase transition, being disordered for u identical with U/NN> or =u(c)(alpha,d) and ordered otherwise [U identical with total energy and N identical with (N(1-alpha/d)-alpha/d)/(1-alpha/d)]. We focus on the nonextensive case alpha/d< or =1 and observe that, for u<u(c), a basin of attraction exists for the initial conditions for which the system quickly relaxes onto a long standing metastable state (whose duration presumably diverges with N-like square root[N]) which eventually crosses over to the microcanonical Boltzmann-Gibbs stable state. It is exhibited that the appropriately scaled maximal Lyapunov exponent lambda(max)(u<u(c))(metastable) proportional, variant N(-kappa(metastable));(N--> infinity ), where, for all values of alpha/d, kappa(metastable) numerically coincides with one third of its value for u>u(c), hence decreases from 1/9 to zero when alpha/d increases from zero to unity, remaining zero thereafter. This simple connection between anomalies above and below the critical point reinforces the nonextensive universality scenario.