Symmetric conserved-mass aggregation model with a mass threshold

Abstract

We study a symmetric conserved-mass aggregation (SCA) model with a mass threshold m(c)(>1). In the SCA model, each site may have any integer mass m, which is active for m >= m(c) and inactive otherwise. For active masses, random toppling of a unit of mass takes place with a rate lambda. An active mass randomly moves to the one of the nearest neighbors with a unit rate and aggregates with a mass on the target site. The SCA model undergoes absorbing phase transition (APT) depending on lambda. The SCA model shares the same features as Manna class, so its critical behaviors are expected to belong to Manna class, if APTs occur. For m(c) = 2, it is shown that the SCA model exhibits the same kinetics of A + A -> A for omega less than or similar to 0.5 and A + B -> at omega = 1 without any transitions, where omega = lambda/(1 + lambda). For 0.5 <= w < 1, APT is shown to occur at a critical rho(c)(omega). The critical decay is similar to that of previous studies for random IC. However, for regular IC, the critical decay exponent agrees with the known results of natural IC, which are close to the value of the directed percolation (DP) class. Off-critical scaling exponents are also shown to be consistent with previous results of natural and regular ICs which are close to DP values. The present study suggests a possibility that the interplay of the diffusion of active sites and the random toppling processes can had to the same critical decay for both regular and natural ICs unlike the decay of models without the interplay.