Tuning spreading and avalanche-size exponents in directed percolation with modified activation probabilities

TL;DR

This paper investigates how adjusting initial activation probabilities in directed percolation can restore criticality and alter spreading exponents, revealing a continuous dependence on these parameters and the presence of multiple absorbing states.

Contribution

It demonstrates that criticality in directed percolation can be maintained by compensating initial activation probability changes with second-time activation adjustments, affecting spreading exponents.

Findings

Criticality can be restored by compensating p1 with p2.

Bulk exponents remain unchanged at compensation.

Spreading exponents vary continuously with (p1, p2).

Abstract

We consider the directed percolation process as a prototype of systems displaying a nonequilibrium 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. Criticality is lost as soon as the probability to activate sites at the first attempt, p1, is changed. We show here that criticality can be restored by "compensating" the change in p1 by an appropriate change of the second time activation probability p2 in the opposite direction. At compensation, we observe that the bulk exponents of the process coincide with those of the normal directed percolation process. However, the spreading exponents are changed, and take values that depend continuously on the pair (p1, p2). We interpret this situation by acknowledging that the model with modified initial probabilities has an infinite number of absorbing states.