Critical behavior of a fixed-energy Manna sandpile model for regular initial conditions in one dimension

Abstract

For a fixed-energy (FE) Manna sandpile model in one dimension, we investigate the critical behavior for regular initial conditions in which activities are distributed at regular intervals on average. The FE Manna model conserves the density $\rho$ of total particles and undergoes an absorbing phase transition at a critical ${\rho }_c$. For the regular initial conditions, we show via extensive simulations that the dynamical scaling behaviors differ from those of the random and the natural initial conditions. Off-critical scaling exponents $\beta$ and ${\nu }_{\perp }$ are also measured and shown to agree well with the values of the directed percolation (DP) class as reported by Basu et al. [ Phys. Rev. Lett. 109, 015702 (2012)]. Our results suggest that the dynamical scaling behaviors depend on the characteristics of initial conditions, but the off-critical scaling behaviors in the steady state are independent of initial conditions and belong to the DP class.