d-Dimensional Classical Heisenberg Model with Arbitrarily-Ranged Interactions: Lyapunov Exponents and Distributions of Momenta and Energies

We numerically study the first-principle dynamics and thermostatistics of a d-dimensional classical inertial Heisenberg ferromagnetic model ([Formula: see text]) with interactions decaying with the distance [Formula: see text] as [Formula: see text] ([Formula: see text]), where the limit [Formula: see text] ([Formula: see text]) corresponds to infinite-range (nearest-neighbour) interactions, and the ratio [Formula: see text] ([Formula: see text]) characterizes the short-ranged (long-ranged) regime. By means of first-principle molecular dynamics we study: (i) The scaling with the system size [Formula: see text] of the maximum Lyapunov exponent [Formula: see text] in the form [Formula: see text] , where [Formula: see text] depends only on the ratio [Formula: see text]; (ii) The time-averaged single-particle angular momenta probability distributions for a typical case in the long-range regime [Formula: see text] (which turns out to be well fitted by q-Gaussians), and (iii) The time-averaged single-particle energies probability distributions for a typical case in the long-range regime [Formula: see text] (which turns out to be well fitted by q-exponentials). Through the Lyapunov exponents we observe an intriguing, and possibly size-dependent, persistence of the non-Boltzmannian behavior even in the [Formula: see text] regime. The universality that we observe for the probability distributions with regard to the ratio [Formula: see text] makes this model similar to the [Formula: see text]-XY and [Formula: see text]-Fermi-Pasta-Ulam Hamiltonian models as well as to asymptotically scale-invariant growing networks.