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 (a $ 0). We show that for N ! ` (thermodynamic limit): (i) The energy per particle EN yN scales like N ; sN12a 2 1dys1 2 ad; (ii) The properly scaled maximum Lyapunov exponent l N tends, for ENysNNd above a threshold, to zero for and only for a # 1. These results are analogous to those observed in lowdimensional and in self-organized critical dissipative systems. This entire picture suggests a connection with the nonextensive thermostatistics recently introduced by one of us. [S0031-9007(98)06314-5]