Breakdown of exponential sensitivity to initial conditions: Role of the range of interactions

Within a microcanonical scenario we numerically study an N-sized linear chain classical inertial XY model including ferromagnetic couplings which decrease with distance as r(-alpha) (alpha greater than or equal to 0). We show that for N-->infinity (thermodynamic limit): (i) The energy per particle E-N/N scales like N* = (N1-alpha -1)/(1 - alpha); (ii) The properly scaled maximum Lyapunov exponent <(lambda)over tilde>(max)(N) tends, for E-N/(NN*) above a threshold, to zero for and only for alpha less than or equal to 1. These results are analogous to those observed in low-dimensional and in self-organized critical dissipative systems. This entire picture suggests a connection with the nonextensive thermostatistics recently introduced by one of us.