Order-parameter critical exponent of absorbing phase transitions in one-dimensional systems with two symmetric absorbing states

Park, Su‐Chan

doi:10.1103/physreve.101.052114

Cited by 2 publications

(3 citation statements)

References 29 publications

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“…A scaling-collapse plot can be used to check the consistency of the estimate of φ. supports the recent estimate of ν in Ref. [29].…”

Section: Two Offspringsupporting

confidence: 92%

“…If q is fixed to be q 0 , the scaling function (24) suggests that plots of ρt δDI against t|ε| ν /φ should collapse onto a single curve for small |ε|. Using ν = 3.55 [29], we get ν /φ ≈ 3.15. A scaling-collapse plot can be used to check the consistency of the estimate of φ. supports the recent estimate of ν in Ref.…”

Section: Two Offspringmentioning

confidence: 87%

“…where q 0 is the critical point for ε = 0; δ DI and ν are the critical exponent of the DI class; and φ is the crossover exponent. In a recent study [29], ν is found to be 3.55 and we will use this value for a data-collapse plot.…”

Section: Two Offspringmentioning

confidence: 99%

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Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors

Park¹

2020

Preprint

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We study absorbing phase transitions in the one-dimensional branching annihilating random walk with long-range repulsion. The repulsion is implemented as hopping bias in such a way that a particle is more likely to hop away from its closest particle. The bias strength due to long-range interaction has the form εx −σ , where x is the distance from a particle to its closest particle, 0 ≤ σ ≤ 1, and the sign of ε determines whether the interaction is repulsive (positive ε) or attractive (negative ε). A state without particles is the absorbing state. We find a threshold εs such that the absorbing state is dynamically stable for small branching rate q if ε < εs. The threshold differs significantly, depending on parity of the number ℓ of offspring. When ε > εs, the system with odd ℓ can exhibit reentrant phase transitions from the active phase with nonzero steady-state density to the absorbing phase, and back to the active phase. On the other hand, the system with even ℓ is in the active phase for nonzero q if ε > εs. Still, there are reentrant phase transitions for ℓ = 2. Unlike the case of odd ℓ, however, the reentrant phase transitions can occur only for σ = 1 and 0 < ε < εs. We also study the crossover behavior for ℓ = 2 when the interaction is attractive (negative ε), to find the crossover exponent φ = 1.123(13) for σ = 0.

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“…A scaling-collapse plot can be used to check the consistency of the estimate of φ. supports the recent estimate of ν in Ref. [29].…”

Section: Two Offspringsupporting

confidence: 92%

Section: Two Offspringmentioning

confidence: 87%

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Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors

Park¹

2020

Preprint

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Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors

Park

2023

J. Korean Phys. Soc.

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Order-parameter critical exponent of absorbing phase transitions in one-dimensional systems with two symmetric absorbing states

Cited by 2 publications

References 29 publications

Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors

Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors

Branching annihilating random walk with long-range repulsion: logarithmic scaling, reentrant phase transitions, and crossover behaviors

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