Vanishing order-parameter critical fluctuations of an absorbing-state transition driven by long-range interactions

Abstract

We study the critical behavior of the absorbing-state phase transition depicted by a contact process one-dimensional model system with power-law decaying interactions. The system dynamical processes include particle creation at a rate which decays with the distance from the nearest particle as $1/{r}^{\ensuremath{\alpha}}$. This model displays an absorbing-state phase transition with critical exponents varying continuously with the interaction exponent $\ensuremath{\alpha}$. Here, we provide a finite-size scaling analysis of the stationary order-parameter density, one of its moment ratio, its logarithmic derivative, and fluctuations. We also follow the short-time relaxation dynamic of these quantities to estimate their corresponding dynamical critical exponents. The estimated exponents are shown to be consistent with the hyperscaling relation. Further, we report an unconventional regime on which the critical order-parameter fluctuations vanish in the thermodynamic limit.