1207.5855 (F. Landes et al.)

Tuning spreading and avalanche size exponents in directed percolation
with modified activation probabilities    [PDF]

F. Landes, E. A. Jagla, Alberto Rosso

We consider the directed percolation process as a prototype of a system displaying a non-equilibrium phase transition into an absorbing state. The model is in a critical state when the activation probability is adjusted at some precise value $p_c$. It is known that this criticality is lost as soon as the probability to activate sites for the first time $p_1$ is changed. We show here that criticality can be restored by "compensating" the change in $p_1$ by a change of the second time activation probability $p_2$ in the opposite direction. At compensation, we observe that the bulk exponent of the process coincide with those of a normal directed percolation process. Instead, the spreading exponents are changed, and take values that depend continuously on the pair $p_1$-$p_2$. We interpret this situation by recognizing that the model with modified initial probabilities is one with an infinite number of absorbing states. We mention the possibility to apply this modified directed percolation model to the understanding of the size distribution of seismic events.

View original: http://arxiv.org/abs/1207.5855