  Miscellaneous magnetic systems are being recently intensively investigated
because of their potential applications in modern technologies. Nonetheless, a
many body dynamical description of complex magnetic systems may be cumbersome,
especially when the system exhibits a geometrical frustration. This paper deals
with simulations of the classical XY model on a three dimensional triangular
lattice with anisotropic couplings, including an analysis of the phase diagram
and a Bogoliubov description of the dynamical stability of mean-field
stationary solutions. We also discuss the possibilities of the realization of
Bose-Hubbard models with complex tunneling amplitudes in shaken optical
lattices without breaking the generalized time-reversal symmetry and the
opposite, i.e. real tunneling amplitudes in systems with the time-reversal
symmetry broken.
