  We study the zero temperature steady state of the random field Blume Capel
model with spin-flip Glauber dynamics on a random regular graph. The
magnetization m as a function of the external field H is observed to have
double hysteresis loops with a return point memory. We also solve the model on
a Bethe lattice in the approximation that the spin relaxation dynamics is
abelian and find good agreement between simulations on random regular graphs
and Bethe lattice calculations for negative values of H.
