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 = 1/2Sigma(i=1)(N)L(i)(2)+Sigma(inot equalj)[1-cos(theta(i)-theta(j))]/r(ij)(alpha); (alphagreater than or equal to0), known to exhibit a second order phase transition, being disordered for u=U/N (N) over tilde greater than or equal tou(c)(alpha,d) and ordered otherwise [U= total energy and (N) over tilde=(N1-alpha/d-alpha/d)/(1-alpha/d)]. We focus on the nonextensive case alpha/dless than or equal to1 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 root<(N)over tilde>) which eventually crosses over to the microcanonical Boltzmann-Gibbs stable state. It is exhibited that the appropriately scaled maximal Lyapunov exponent lambda(u<uc)(max)(metastable)proportional toN(metastable)(-kappa);(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.