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

Abstract

We present the numerical study of chaos in a classical model of N coupled rotators on a lattice, in dimensions d=2,3. The coupling constants decay with distance as r ij − α ( α⩾0). The thermodynamics of the model is extensive if α/ d>1 and nonextensive otherwise. For energies above a critical threshold U c the largest Lyapunov exponent scales as N − κ , where κ is a universal function of α/ d. The function κ decreases from 1/3 to 0 when α/ 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).