  A one dimensional classically chaotic spin chain with asymmetric coupling and
two different inter-spin interactions, nearest neighbors and all-to-all, has
been considered. Depending on the interaction range, dynamical properties, as
ergodicity and chaoticity are strongly different. Indeed, even in presence of
chaoticity, the model displays a lack of ergodicity only in presence of all to
all interaction and below an energy threshold, that persists in the
thermodynamical limit. Energy threshold can be found analytically and results
can be generalized for a generic XY model with asymmetric coupling.

Statistical Mechanics