  We calculate analytically the largest Lyapunov exponent of the so-called
$\alpha XY$ Hamiltonian in the high energy regime. This system consists of a
$d$-dimensional lattice of classical spins with interactions that decay with
distance following a power-law, the range being adjustable. In disordered
regimes the Lyapunov exponent can be easily estimated by means of the
"stochastic approach", a theoretical scheme based on van Kampen's cumulant
expansion. The stochastic approach expresses the Lyapunov exponent as a
function of a few statistical properties of the Hessian matrix of the
interaction that can be calculated as suitable microcanonical averages. We have
verified that there is a very good agreement between theory and numerical
simulations.
