Abstract

Classical spin models have called the attention of many researchers in the last decades. Such is the case of two instances of the so called n-vector classical spin model: the XY (n=2) and Heisenberg (n=3) models. In our formulation a kinetic term is introduced in the Hamiltonian so the spin variables may be interpreted as classical rotators. The inertial ferromagnetic XY model (mostly referred to as Hamiltonian Mean Field model) has been extensively studied since its introduction by Antoni and Ruffo in 1995 and has become paradigmatic in the study of the dynamical behavior of classical many-body Hamiltonian systems. The model was subsequently generalized to the so called a-XY model by Anteneodo and Tsallis by means of the introduction of an interaction term depending as a power law on the distance between rotators. In the long-range regime the model presents unusual features as breakdown of ergodicity, ensemble inequivalence, long lived quasistationary states and non-Gaussian probability distributions. This model, as well as its much less studied generalization to 3d rotators, the a-Heisenberg model, will be studied within the framework of Nonextensive Statistical Mechanics, a current generalization of Boltzmann-Gibbs Statistical Mechanics specially suited to deal with out-of-equilibrium and long-range correlated models.