  We analyze the steady state regime of systems interpolating between spin
glasses and ferromagnets under a tapping dynamics recently introduced by
analogy with the dynamics of mechanically perturbed granular media. A crossover
from a second order to first order ferromagnetic transition as a function of
the spin coupling distribution is found. The flat measure over blocked states
introduced by Edwards for granular media is used to explain this scenario.
Annealed calculations of the Edwards entropy are shown to qualitatively explain
the nature of the phase transitions. A Monte-Carlo construction of the Edwards
measure confirms that this explanation is also quantitatively accurate.
