Criticality of natural absorbing states - art. no. 031107

We study a recently introduced ladder model that undergoes a transition bet ween an active and an infinitely degenerate absorbing phase. In some cases the critical behavior of the model is the same as that of the branching-ann ihilating random walk with N greater than or equal to2 species both with an d without hard-core interaction. We show that certain static characteristic s of the so-called natural absorbing states develop power-law singularities that signal the approach of the critical point. These results are also exp lained using random-walk arguments. In addition to that we show that when d ynamics of our model is considered as a minimum-finding procedure, it has t he best efficiency very close to the critical point.