Classical spin systems with long-range interactions: universal reduction of mixing

We present the numerical study of chaos in a classical model of N coupled r otators on a lattice, in dimensions d = 2, 3. The coupling constants decay with distance as r(ij)(-alpha) (alpha greater than or equal to 0). The ther modynamics of the model is extensive if alpha /d > 1 and nonextensive other wise. For energies above a critical threshold U-c the largest Lyapunov expo nent scales as N-kappa, where kappa is a universal function of alpha /d. Th e function kappa decreases from 1/3 to 0 when alpha /d increases from 0 to 1, and vanishes above 1. We conjecture that this scaling law is related to the nonextensivity of the model, through a power-law sensitivity to initial conditions (weak mixing). (C) 2001 Published by Elsevier Science B.V.