Dynamics of the classical Heisenberg spin chain

Abstract

In this paper the authors study the evolution equations for the classical discrete anisotropic Heisenberg spin chain. In the continuum limit these equations become completely integrable and are related to well known equations such as the sine-Gordon and non-linear Schrodinger equations. Some particular solutions of the discrete equations are presented, including spin waves, spatially homogeneous solutions and planar states which provide an example of a completely integrable mapping. A linear stability analysis, some numerical studies and particular time-dependent solutions suggest that, for certain regions of phase space and parameter values, the system possesses chaotic solutions.