From quasi-stationary states to multi-absorbing states growth model.

A one-dimensional growth model with local absorption and nonlocal desorption is studied. Its phase diagram is characterized by two parameters, one controlling the temporal correlation and the other describing the ratio between the absorbing and desorbing rates. Depending on the parameters, the stochastic model exhibits either self-organized criticality, quasi-stationarity, multi-absorbing transitions or massive behaviors. Two boundaries are of special interest: the first separates the region with self-organized criticality from the one of massive behavior, and it corresponds to a conformal invariant growth model. The second divides the regions of quasi-stationarity and of multi-absorption phase and it appears as a critical line in the phase diagram.

In the non-equilibrium regime, we observe quasi-stationary states with an exponential increase in the lifetime as a function of the size system, a behavior typical of activated dynamical scaling. In the no-absorption case, the dynamics of the surface can be derived analytically and exhibits a transient dynamic whose timescale is much larger than the expected lifetime of $1/E_1$, with $E_1$ the energy gap. This timescale behaves like a "critical initial slip" and strongly depends on the size of the biggest cluster in the initial condition. This highlights the need of controlling the typical size of the clusters in the initial conditions, otherwise the estimation of dynamical exponents may be erroneous.

Finally, we observe deviations from the conformal tower in the no-absorption case when investigating the critical transition from the absorbing to the multi-absorbing phase, as an additional parameter in the model in tuned.