Criticality of natural absorbing states
A. Lipowski1 , M. Droz2
1 Department of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614, Poznań, Poland
2 Département de Physique Théorique, Université de Genève, CH 1211 Genève 4, Switzerland
Physical Review E, 64, 031107 (2001)
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.