  Models undergoing a phase transition to an absorbing state weakly broken by
the addition of a very low spontaneous nucleation rate are shown to exhibit
hysteresis loops whose width $\Delta\lambda$ depends algebraically on the ramp
rate $r$. Analytical arguments and numerical simulations show that
$\Delta\lambda \sim r^{\kappa}$ with $\kappa = 1/(\beta'+1)$, where $\beta'$ is
the critical exponent governing the survival probability of a seed near
threshold. These results explain similar hysteresis scaling observed before in
liquid crystal convection experiments. This phenomenon is conjectured to occur
in a variety of other experimental systems.
