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 Deltalambda depends algebraically on the ramp rate r . Analytical arguments and numerical simulations show that Deltalambda approximately 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.