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^-α ( α≥0). We show that for N→∞ (thermodynamic limit): (i) The energy per particle EN/N scales like N*≡(N^1-α-1)/(1-α); (ii) The properly scaled maximum Lyapunov exponent ̃ \~λNᵐᵃˣ tends, for EN/(NN*) above a threshold, to zero for and only for α≤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.