The relaxation of initial condition in systems with infinitely many absorbing states

TL;DR

This paper studies how initial conditions affect spreading exponents in one-dimensional models with many absorbing states, revealing slow relaxation effects and initial condition dependencies.

Contribution

It demonstrates the impact of initial conditions on critical exponents and transition points in PCP and TTP models, highlighting slow relaxation of non-order fields.

Findings

Non-order field exhibits critical fluctuations and relaxes with the same power-law as the order parameter.

Transition point location depends slightly on initial concentration in PCP.

Damage spreading exponents match those of the ordinary critical point.

Abstract

We have investigated the effect of the initial condition on the spreading exponents of the one-dimensional 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.