Continuously varying critical order-parameter fluctuations in a parity conserving absorbing-state transition with long-range diffusion

Abstract

We study the critical order parameter fluctuations of the absorbing-state phase-transition exhibited by branching and annihilating random walkers performing anomalous diffusion in a linear chain. The diffusion process is considered to follow a power-law distribution of jump lengths with a typical decay exponent α. We focus in the case of parity conserving dynamics for which deviations from the usual directed percolation universality class have been previously demonstrated even for the limiting cases of normal diffusion. Anomalous diffusion induces a continuous change of the critical exponents. By performing a finite-size scaling analysis of simulation data, we show that the critical order parameter moment ratio also varies continuously with α. We unveil that the critical order parameter distribution evolves from a nearly Gaussian to an exponential form as the range of the jump distribution is increased up to the limit on which the active state predominates for any finite branching probability.