We consider the class of long-range Hamiltonian systems first introduced by
Anteneodo and Tsallis and called the alpha -XY model. This involves N clas
sical rotators on a d-dimensional periodic lattice interacting all to all w
ith an attractive coupling whose strength decays as r(-alpha), r being the
distance between sites. Using a recent geometrical approach, we estimate fo
r any d-dimensional lattice the scaling of the largest Lyapunov exponent (L
LE) with N, as a function of a in the large energy regime where rotators be
have almost freely. We find that the LLE vanishes as N-kappa, with kappa =
1/3 for 0 less than or equal to alpha /d less than or equal to 1/2 and kapp
a = 2/3(1 - alpha /d) for 1/2 less than or equal to alpha /d < 1. These ana
lytical results present a nice agreement with numerical results obtained by
Campa et al, including deviations at small N.