Systems with superabsorbing states

We report on some extensive analyses of a recently proposed model [A. Lipow ski, Phys. Rev. E 60, 6255 (1999)] with infinitely many absorbing states. B y performing extensive Monte Carlo simulations, we have determined critical exponents and shown strong evidence that this model is not in the directed percolation universality class. The conjecture that this two-dimensional m odel exhibits a dimensional reduction (behaving as one-dimensional directed percolation) is firmly disproven. The reason for the model not exhibiting standard directed percolation scaling behavior is traced back to the existe nce of what we call superabsorbing sites, i.e., absorbing sites that cannot be directly activated by the presence of neighboring activity in one or mo le than one direction. Supporting this claim we present two strong evidence s: (i) in one dimension, where superabsorbing sites do not appear at the cr itical point, the system behaves as directed percolation, and (ii) in a mod ified two-dimensional variation of the model, defined on a honeycomb lattic e, for which superabsorbing sites are very rarely observed, directed percol ation behavior is recovered. Finally, a parallel updating version of the mo del exhibiting a nonequilibrium first-order transition is also reported.