Scaling of hysteresis loops at phase transitions into a quasiabsorbing state

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.