Controlling the range of interactions in the classical inertial ferromagnetic Heisenberg model: analysis of metastable states

A numerical analysis of a one-dimensional Hamiltonian system, composed by N classical localized Heisenberg rotators on a ring, is presented. A distance r(ij) between rotators at sites i and j is introduced, such that the corresponding two-body interaction decays with rij as a power-law, 1/r(ij)(alpha) (alpha >= 0). The index a controls the range of the interactions, in such a way that one recovers both the fully-coupled (i.e. mean-field limit) and nearest-neighbour-interaction models in the particular limits alpha = 0 and alpha -> infinity, respectively. The dynamics of the model is investigated for energies U below its critical value (U < U-c) , with initial conditions corresponding to zero magnetization. The presence of quasi-stationary states (QSSs), whose durations t(QSS) increase for increasing values of N, is verified for values of a in the range 0 <= alpha < 1, like the ones found for the similar model of XY rotators. Moreover, for a given energy U, our numerical analysis indicates that tQSS similar to N-gamma, where the exponent gamma decreases for increasing a in the range 0 <= alpha< 1 and particularly, our results suggest that gamma -> 0 as alpha -> 1. The growth of t(QSS) with N could be interpreted as a breakdown of ergodicity, which is shown herein to occur for any value of a in this interval.