Quasi-stationary states in nonlocal stochastic growth models with infinitely many absorbing states

We study a two parameter (u, p) extension of the conformally invariant raise and peel model. The model also represents a nonlocal and biased-asymmetric exclusion process with local and nonlocal jumps of excluded volume particles in the lattice. The model exhibits an unusual and interesting critical phase where, in the bulk limit, there are an infinite number of absorbing states. In spite of these absorbing states the system stays, during a time that increases exponentially with the lattice size, in a critical quasi-stationary state. In this critical phase the critical exponents depend only on one of the parameters defining the model (u). The endpoint of this critical phase, where the system changes from an active to an inactive frozen phase, belongs to a distinct universality class. This new behavior, we believe, is due to the appearance of Jordan cells in the Hamiltonian describing the time evolution. The dimensions of these cells increase with the lattice size. In a special case (u = 0) where the model has no adsorptions we are able to calculate analytically the time evolution of some observables. A polynomial time dependence is obtained thanks to the appearance of Jordan cells structures in the Hamiltonian.