PHYSICAL REVIEW E 105, 025307 (2022)

Jin Min Kim * and Sang Bub Lee †
Department of Physics and OMEG Institute, Soongsil University, Seoul 06978, Korea

(Received 13 August 2021; accepted 26 January 2022; published 9 February 2022)
We applied an alternative method for measuring characteristic lengths reported recently by one of us [J. M. Kim, J. Stat. Mech. (2021) 033213] to the models in the Manna universality class, i.e., the stochastic Manna sandpile and conserved lattice gas models in various dimensions.

The universality of the Manna model has been under long debate particularly in one dimension since the work of M. Basu et al. [Phys. Rev. Lett. 109,015702 (2012)], who claimed that the Manna model belongs to the directed percolation (DP) universality class and that the independent Manna universality class does not exist. We carried out Monte Carlo simulations for the stochastic Manna sandpile model in one, two, and three dimensions and the conserved lattice gas model in three dimensions, using both the natural initial states (NISs) and uniform initial states (UISs).  In two and three dimensions, the results for R(t ), defined by R(t ) = L[ρ2a/ρa2 − 1]1/d , L and ρa being, respectively, the system size and activity density, yielded consistent results for the two initial states. R(t ) is proportional to the correlation length following R(t ) ∼ t 1/z at the critical point. In one dimension, the data of R(t ) for the Manna model using NISs yielded anomalous behavior, suggesting that NISs require much longer prerun time steps to homogenize the distribution of particles and larger systems to eliminate the finite-size effect than those employed in the literature. On the other hand, data from UISs yielded a power-law behavior, and the estimated critical exponents differed from the values in the DP class.

DOI:  https://doi.org/10.1103/PhysRevE.105.025307