Comment on “Dependence of asymptotic decay exponents on initial condition and the resulting scaling violation”

Kwon, Sungchul; Kim, Jin Min

doi:10.1103/physreve.90.046101

Cited by 7 publications

(3 citation statements)

References 7 publications

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“…However, for ρ < 1, total mass is smaller than the number of empty sites (ρ A (0) < ρ B (0)), so the system eventually falls into one of absorbing states consisting of empty sites and inactive sites of m = 1. As a result, in terms of A + B → 0 reaction, the SCA model undergoes the crossover at ρ = 1 from the kinetics of ρ A (0) > ρ B (0) to that of ρ A (0) = ρ B (0) for ρ → 1 + as shown for conserved lattice gas (CLG) model in d = 1 [49,50].…”

Section: ω = 1 Andmentioning

confidence: 90%

“…It is shown that the dynamics of active masses is eectively considered as A + A → A reaction for ω < ω 0 (≈ 0.5), and A + B → 0 reaction at ω = 1. Since the reproduction of particles and the mutation to the other species are not allowed in both reactions [47][48][49][50], APTs cannot take place for ω < ω 0 and ω = 1 in the SCA model. For ω 0 ω < 1, however, APT is shown to occur due to the competition of aggregation and chipping processes, and ρ c continuously increases with ω.…”

Section: J Stat Mech (2018) 113204mentioning

confidence: 99%

“…In A + B → 0 reaction with equal initial density of two species, i.e. ρ A (0) = ρ B (0), the density of each species decays as t −1/4 for random IC and t −1/2 for regular IC such as (ABAB • • • ) in d = 1 regardless of mobility of one species [47][48][49][50]. The dierent decay exponents result from the domain structure generated by random initial fluctuations and the alternating distribution of opposite species for which the reaction just becomes a single species reaction A + A → 0 [47,48].…”

Section: ω = 1 Andmentioning

confidence: 99%

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Symmetric conserved-mass aggregation model with a mass threshold

Kwon¹,

Kim²

2018

J. Stat. Mech.

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We study a symmetric conserved-mass aggregation (SCA) model with a mass threshold mc(>1). In the SCA model, each site may have any integer mass m, which is active for and inactive otherwise. For active masses, random toppling of a unit of mass takes place with a rate λ. 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 λ. 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 mc = 2, it is shown that the SCA model exhibits the same kinetics of for and at without any transitions, where . For , APT is shown to occur at a critical . 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 lead to the same critical decay for both regular and natural ICs unlike the decay of models without the interplay.

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Section: ω = 1 Andmentioning

confidence: 90%

Section: J Stat Mech (2018) 113204mentioning

confidence: 99%

Section: ω = 1 Andmentioning

confidence: 99%

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Symmetric conserved-mass aggregation model with a mass threshold

Kwon¹,

Kim²

2018

J. Stat. Mech.

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Effects of random initial conditions on the dynamical scaling behaviors of a fixed-energy Manna sandpile model in one dimension

Kwon

Kim

2015

Phys. Rev. E

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For a fixed-energy (FE) Manna sandpile model in one dimension, we investigate the effects of random initial conditions on the dynamical scaling behavior of an order parameter. In the FE Manna model, the density ρ of total particles is conserved, and an absorbing phase transition occurs at ρ(c) as ρ varies. In this work, we show that, for a given ρ, random initial distributions of particles lead to the domain structure in which domains with particle densities higher and lower than ρ(c) alternate with each other. In the domain structure, the dominant length scale is the average domain length, which increases via the coalescence of adjacent domains. At ρ(c), the domain structure slows down the decay of an order parameter and also causes anomalous finite-size effects, i.e., power-law decay followed by an exponential one before the quasisteady state. As a result, the interplay of particle conservation and random initial conditions causes the domain structure, which is the origin of the anomalous dynamical scaling behaviors for random initial conditions.

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Absorbing phase transition in a conserved lattice gas model with next-nearest-neighbor hopping in one dimension

Lee

2015

Phys. Rev. E

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The absorbing phase transition of the modified conserved lattice gas (m-CLG) model was investigated in one dimension. The m-CLG model was modified from the conserved lattice gas (CLG) model in such a way that each active particle hops to one of the nearest-neighbor and next-nearest-neighbor empty sites. The order parameter exponent, the dynamic exponent, and the correlation length exponent were estimated from the power-law behavior and finite-size scaling of the active particle densities. The exponents were found to differ considerably from those of the ordinary CLG model and were also distinct from those of the Manna model, suggesting that next-nearest-neighbor hopping is a relevant factor that alters the critical behavior in the one-dimensional CLG model.

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Comment on “Dependence of asymptotic decay exponents on initial condition and the resulting scaling violation”

Cited by 7 publications

References 7 publications

Symmetric conserved-mass aggregation model with a mass threshold

Symmetric conserved-mass aggregation model with a mass threshold

Effects of random initial conditions on the dynamical scaling behaviors of a fixed-energy Manna sandpile model in one dimension

Absorbing phase transition in a conserved lattice gas model with next-nearest-neighbor hopping in one dimension

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