Abstract

We numerically study the first-principle dynamics and thermostatistics of a d-dimensional classical inertial Heisenberg ferromagnetic model ( $d=1,2,3$ ) with interactions decaying with the distance $r_{ij}$ as $1/r_{ij}^{\alpha }$ ( $\alpha \ge 0$ ), where the limit $\alpha =0$ ( $\alpha \to \infty$ ) corresponds to infinite-range (nearest-neighbour) interactions, and the ratio $\alpha /d>1$ ( $0\le \alpha /d\le 1$ ) characterizes the short-ranged (long-ranged) regime. By means of first-principle molecular dynamics we study: (i) The scaling with the system size $\mathcal{N}$ of the maximum Lyapunov exponent $\lambda$ in the form $\lambda \sim {\mathcal{N}}^{-\kappa }$ , where $\kappa (\alpha /d)$ depends only on the ratio $\alpha /d$ ; (ii) The time-averaged single-particle angular momenta probability distributions for a typical case in the long-range regime $0\le \alpha /d\le 1$ (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 $0\le \alpha /d\le 1$ (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 $\alpha /d>1$ regime. The universality that we observe for the probability distributions with regard to the ratio $\alpha /d$ makes this model similar to the $\alpha$ -XY and $\alpha$ -Fermi-Pasta-Ulam Hamiltonian models as well as to asymptotically scale-invariant growing networks. View Full-Text