Relaxation of initial conditions in systems with infinitely many absorbing states

Abstract

We have investigated the effect of the initial condition on the spreading exponents of the onedimensional pair contact process (PCP) and threshold transfer process (TTP).The non-order field was found to exhibit critical fluctuations, relaxing to its natural value with the same power-law as the order parameter field. We argue that this slow relaxation, which was not taken into account in earlier studies of these models, is responsible for the continuously changing survival probability exponent. High precision numerical simulations show evidence of a (slight) dependence of the location of the transition point on the initial concentration, in the case of PCP. The damage spreading (DS) point and the spreading exponents coincide with those of the ordinary critical point in both cases.

Nonuniversality in the pair contact process with diffusion

“…While the absorbing state in the contact process corresponds to a unique configuration (an empty lattice), the PCP possesses infinitely many absorbing configurations. Numerical and theoretical studies nevertheless indicate that the PCP belongs to the same universality class as the CP (namely, that of directed percolation (DP)), but with anomalies in the critical spreading dynamics [1,2,[6][7][8][9][10][11][12]]. An infinite number of absorbing configurations arise in the PCP because all processes (creation and annihilation), require a nearest-neighbor (NN) pair of particles (to be referred to simply as a "pair" in what follows).…”

Static critical behavior in the inactive phase of the pair contact process

“…In PCP, as the system approaches the critical point from the active phase, the nonordering field approaches a 'natural' value (ρ nat 1 ), and its behavior is described by the same power laws as those of the order parameter [10].…”

Universality class of absorbing transitions with continuously varying critical exponents

“…the Domany-Kinzel cellular automaton [10], the Ziff-Gulari-Barshad model for a surface catalytic reaction [11], the branching-annihilating random walks with an odd number of offspring [12], and the pair contact process (PCP) [13]. Unlike others, the PCP has infinitely many absorbing states, which leads to controversial transient behaviors, i.e., nonuniversal scaling [13,14,15,16] versus absence of scaling [17,18]. But its stationary critical behavior still belongs to the DP class at low dimensions [19].…”