Universality classes of absorbing phase transitions in generic branching-annihilating particle systems with nearest-neighbor bias

Daga, Bijoy; Ray, Purusattam

doi:10.1103/physreve.99.032104

Cited by 14 publications

(31 citation statements)

References 38 publications

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“…We have concluded that a continuous phase transition takes place at ε ′ = 0.25. ρ(t → ∞) behaves as an order parameter that vanishes continuously as (ε ′ c − ε ′ ) β . The phase transition is similar to that studied recently in [34]. The presence of a diverging length scale as well as a diverging timescale have been detected as ε c ′ → 0.25 with exponents ν ≈ 1 and z lying between 2.1 and 2.2, obtained using several different finite size scaling analyses.…”

Section: Discussion and Concluding Remarkssupporting

confidence: 84%

Effect of bias in a reaction-diffusion system in two dimensions

Mullick

Sen

2019

Phys. Rev. E

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We consider a single species reaction diffusion system on a two dimensional lattice where the particles A are biased to move towards their nearest neighbours and annihilate as they meet. Allowing the bias to take both negative and positive values parametrically, any nonzero bias is seen to drastically affect the behaviour of the system compared to the unbiased (simple diffusive) case. For positive bias, a finite number of dimers, which are isolated pairs of particles occurring as nearest neighbours, exist while for negative bias, a finite density of particles survives. Both the quantities vanish in a power law manner close to the diffusive limit with different exponents. The appearance of dimers is exclusively due to the parallel updating scheme used in the simulation. The results indicate the presence of a continuous phase transition at the diffusive point. In addition, a discontinuity is observed at the fully positive bias limit. The persistence behaviour is also analysed for the system.

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Section: Discussion and Concluding Remarkssupporting

confidence: 84%

Effect of bias in a reaction-diffusion system in two dimensions

Mullick

Sen

2019

Phys. Rev. E

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“…Therefore, it is concluded that the different critical behavior from the DI class in Ref. [21] is attributed to the long-range nature of the local bias.…”

Section: Introductionmentioning

confidence: 81%

“…[17][18][19] When a global hopping bias is introduced to the BAW in such a way that hopping along a predefined direction is preferred (for example, in one dimension hopping to the right has larger transition rate than hopping to the left), this bias in the (asymptotic) field theory is gauged away by a Galilean transformation [20] and, in turn, critical behavior is not affected by the global bias. Recently, a local hopping bias is introduced to the BAW [21] in such a manner that a particle prefers hopping toward the nearest particle. Since a particle is likely to get close to the nearest particle by the local bias, this form of interaction associated with the local bias is termed as attraction in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Branching annihilating random walks with long-range attraction in one dimension

Park

2020

Preprint

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We introduce and numerically study the branching annihilating random walks with long-range attraction (BAWL). The long-range attraction makes hopping biased in such a manner that particle's hopping along the direction to the nearest particle has larger transition rate than hopping against the direction. Still, unlike the Lévy flight, a particle only hops to one of its nearest-neighbor sites. The strength of bias takes the form x −σ with nonnegative σ, where x is the distance to the nearest particle from a particle to hop. By extensive Monte Carlo simulations, we show that the critical decay exponent δ varies continuously with σ up to σ = 1 and δ is the same as the critical decay exponent of the directed Ising (DI) universality class for σ ≥ 1. Investigating the behavior of the density in the absorbing phase, we argue that σ = 1 is indeed the threshold that separates the DI and non-DI critical behavior. We also show by Monte Carlo simulations that branching bias with symmetric hopping exhibits the same critical behavior as the BAWL.

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“…When branching is introduced to the AWLA, rich critical phenomena have been reported especially for the case of the even number of offspring [33,38,39]. In this context, it is natural to ask what would happen if branching is introduced to the AWLR.…”

Section: Summary and Discussionmentioning

confidence: 99%

Branching annihilating random walks with long-range attraction in one dimension

Park

2020

Phys. Rev. E

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We study the annihilating random walk with long-range interaction in one dimension. Each particle performs random walks on a one-dimensional ring in such a way that the probability of hopping toward the nearest particle is W = [1 − ε(x + µ) −σ ]/2 (the probability of moving away from its nearest particle is 1 − W), where x is the distance from the hopping particle to its nearest particle and ε, µ, and σ are parameters. For positive (negative) ε, a particle is effectively repulsed (attracted) by its nearest particle and each hopping is generally biased. On encounter, two particles are immediately removed from the system. We first study the survival probability and the mean spreading behaves in the long-time limit if there are only two particles in the beginning. Then, we study how the density decays to zero if all sites are occupied at the outset. We find that the asymptotic behaviors are classified by seven categories; (i) σ > 1 or ε = 0, (ii) σ = 1 and 2ε > 1, (iii) σ = 1 and 2ε = 1, (iv) σ = 1 and 2ε < 1, (v) σ < 1 and ε > 0, (vi) σ = 0 and ε < 0, and (vii) 0 < σ < 1 and ε < 0. The asymptotic behaviors in each category are universal in the sense that µ (and sometimes ε) cannot affect the asymptotic behaviors.

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Universality classes of absorbing phase transitions in generic branching-annihilating particle systems with nearest-neighbor bias

Cited by 14 publications

References 38 publications

Effect of bias in a reaction-diffusion system in two dimensions

Effect of bias in a reaction-diffusion system in two dimensions

Branching annihilating random walks with long-range attraction in one dimension

Branching annihilating random walks with long-range attraction in one dimension

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