We consider the class of long-range Hamiltonian systems first introduced by
Anteneodo and Tsallis and called the alpha-XY model. This involves N classical
rotators on a d-dimensional periodic lattice interacting all to all with an
attractive coupling whose strength decays as r^{-alpha}, r being the distances
between sites. Using a recent geometrical approach, we estimate for any
d-dimensional lattice the scaling of the largest Lyapunov exponent (LLE) with N
as a function of alpha in the large energy regime where rotators behave almost
freely. We find that the LLE vanishes as N^{-kappa}, with kappa=1/3 for alpha/d
between 0 and 1/2 and kappa=2/3(1-alpha/d) for alpha/d between 1/2 and 1. These
analytical results present a nice agreement with numerical results obtained by
Campa et al., including deviations at small N.Comment: 10 pages, 3 eps figure
