Critical behavior for random initial conditions in the one-dimensional fixed-energy Manna sandpile model

Abstract

A fixed-energy Manna sandpile model undergoes an absorbing phase transition at a critical rho(c), where an order parameter phi(t) decays as t(-alpha) in time t. As the prototype of the Manna class, the model has been extensively studied in one dimension. However, the previous estimates of rho(c) and some critical exponents are different, depending on the types of initial conditions; random, natural, and regular conditions. The estimates of rho(c) for the random and the regular conditions are the lower and the upper bound among currently known estimates, respectively. In this work, for the random conditions, rho(c) and a are measured by taking into account finite-size (FS) effects. At the previous estimate of rho(c), simulation results show that the temporal decay of phi(t) is strongly affected by the FS effects up to much larger system size (similar to 10(6)). For the sizes for which phi(t) is independent up to t = 2 x 10(7), we estimate rho(c) = 0.8925(1) and alpha = 0.110(5), which clearly differ from the previous results for the random conditions, rho(c) = 0.89199(5) and alpha = 0.141(24). Instead, the present.c agrees with rho(c) = 0.89255(2) of the regular conditions. In addition, the present a is substantially distinguishable from the results of the other types of initial conditions, alpha = 0.159(3) and 0.146(2) for the natural and the regular conditions, respectively, which supports the claim of the initial condition dependence of dynamical exponents in the Manna class.