title: Criticality of natural absorbing states.
abstract: We study a recently introduced ladder model that undergoes a transition between 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-annihilating random walk with N>/=2 species both with and without hard-core interaction. We show that certain static characteristics of the so-called natural absorbing states develop power-law singularities that signal the approach of the critical point. These results are also explained using random-walk arguments. In addition to that we show that when dynamics of our model is considered as a minimum-finding procedure, it has the best efficiency very close to the critical point.
authors.affiliation: Department of Physics, Adam Mickiewicz University, 61-614 Poznan, Poland. lipowski@main.amu.edu.pl
authors.forename: A
authors.initials: A
authors.lastname: Lipowski
authors.forename: M
authors.initials: M
authors.lastname: Droz