  The present work pursues the investigation of the role of spatial asymmetry
and irreversibility on the dynamical properties of spin systems. We consider
the ferromagnetic spherical model with asymmetric linear Langevin dynamics.
Such an asymmetric dynamics is irreversible, i.e., breaks detailed balance,
because the principle of action and reaction is violated. The
fluctuation-dissipation theorem therefore no longer holds. The stationary state
is however still Gibbsian, i.e., the weights of configurations are given by the
Boltzmann factor corresponding to the ferromagnetic Hamiltonian. The model is
exactly solvable in any dimension, enabling an analytical evaluation of
time-dependent observables. We show the existence of two regimes of violation
of the fluctuation-dissipation theorem in the nonequilibrium stationary state:
a regime of weak violation where the stationary fluctuation-dissipation ratio
is finite but less than unity and varies continuously with the asymmetry, and a
regime of strong violation where the fluctuation-dissipation ratio vanishes
asymptotically. This phenomenon was first uncovered in the asymmetric kinetic
Ising chain. The present results suggest that this novel kind of dynamical
transition in nonequilibrium stationary states might be quite general. We also
perform a systematic analysis of several regimes of interest, either stationary
or transient, in various dimensions and in the different phases of the model.
