  We consider a system of hierarchical interacting spins under dynamics of
spin-flip type with a ferromagnetic mean field interaction, scaling with the
hierarchical distance, coupled with a system of linearly interacting
hierarchical diffusions of Ornstein-Uhlenbeck type. In particular, the
diffusive variables enter in the spin-flip rates, effectively acting as
dynamical magnetic fields. In absence of the diffusions, the spin-flip dynamics
can be thought of as a modification of the Curie--Weiss model. We study the
mean field and the two-level hierarchical model, in the latter case restricting
to a subcritical regime, corresponding to high temperatures, obtaining
macroscopic limits at different spatio-temporal scales and studying the phase
transitions in the system. We also formulate a generalization of our results to
the $k$-th level hierarchical case, for any $k$ finite, in the subcritical
regime. We finally address the supercritical regime, in the zero-temperature
limit, for the two-level hierarchical case, proceeding heuristically with the
support of numerics.
