Pair contact process with a particle source

Dickman, Ronald; Rabelo, Wilson R. M.; Ódor, Géza

doi:10.1103/physreve.65.016118

Cited by 19 publications

(37 citation statements)

References 42 publications

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“…To have access to intervals of particle density smaller than 1/L, we follow a method employed in the study of conserved sandpile models [18] and pair contact process [26]. Initially we determine the stationary average of ρ for a series of discrete values of the particle density, as shown in Fig.…”

Section: Simulationmentioning

confidence: 99%

Conserved Sandpile with A Variable Height Restriction

2013

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We study a restricted-height version of the one-dimensional Oslo sandpile with conserved density, using periodic boundary conditions. Each site has a limiting height which can be either two or three. When a site reaches its limiting height it becomes active and may topple, loosing two particles, which move randomly to nearest-neighbor sites. After a site topples it is randomly assigned a new limiting height. We study the model using meanfield theory and Monte Carlo simulation, focusing on the quasi-stationary state, in which the number of active sites fluctuates about a stationary value. Using finite-size scaling analysis, we determine the critical particle density and associated critical exponents.

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Section: Simulationmentioning

confidence: 99%

Conserved Sandpile with A Variable Height Restriction

2013

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“…We shall not describe the details of the mean-field technique because it has already been applied and demonstrated for the PCP model by several authors previously [5,9,10]. The derivation of the hierarchy of equations of motion for the configuration probabilities on the n-site clusters becomes complicated for large n. The technical difficulties increase drastically when enlarging the size of clusters.…”

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“…The transition point is determined by the zero-point of ρ 2 for h = 0 and by the breaking point of the function ρ 1 (p) for h > 0. This latter criteria was particularly useful because of the extremely low value of ρ 2 in a large interval of p.We shall not describe the details of the mean-field technique because it has already been applied and demonstrated for the PCP model by several authors previously [5,9,10]. The derivation of the hierarchy of equations of motion for the configuration probabilities on the n-site clusters becomes complicated for large n. The technical difficulties increase drastically when enlarging the size of clusters.…”

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confidence: 99%

“…al. introduced a modified PCP model to explore the robustness of DP transition [5]. In this model, each site of the one-dimensional lattice is either vacant or occupied by a single particle.…”

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“…Further details of the model can be found in Ref. [5]. This extended model was studied by Monte Carlo (MC) simulations and dynamical cluster mean-field approximation for quite large cluster sizes (ranged from n = 2 to 6).…”

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Dynamical mean-field approximation for a pair contact process with a particle source

Szolnoki

2002

Phys. Rev. E

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The one-dimensional pair contact process with a particle source is studied by using dynamical cluster mean-field approximations with sites up to n = 12. The results obtained for different levels of approximation become convergent especially for n ≥ 6 and allow us to derive reliable extrapolations to the limit n → ∞. At the zero source limit, the critical point exhibits a discontinuity whose magnitude vanishes with 1/n. The coherent anomaly analysis of data supports that the vanishing of order parameter and density of isolated particles has the same critical behavior. In contrast to an earlier prediction, the present approximation does not support the existence of critical behavior in the inactive phase where the frozen density of isolated particles depends on the initial state.PACS numbers: 02.70. Lq, 05.50.+q, 05.70.Ln, 64.60.Cn The study of phase transitions from active fluctuating phases into absorbing states has attracted considerable interest in the last decade [1,2]. The static exponents of these phase transitions belong frequently to the directed percolation (DP) universality class, however, there are also examples for new universality classes [3]. Open questions are related to the necessary conditions that can destroy this robust universal behavior. One of the simplest model showing static DP behavior is the pair contact process (PCP) which was proposed to realize a system involving infinitely many absorbing states [4]. Recently, Dickman et. al. introduced a modified PCP model to explore the robustness of DP transition [5]. In this model, each site of the one-dimensional lattice is either vacant or occupied by a single particle. A (randomly chosen) pair of nearest-neighbor particles is annihilated with a probability p or an additional particle is created around the given pair with a probability 1 − p if it is not forbidden by double occupancy. In the extended model, an external particle source is introduced that attempts to insert isolated particles with a rate of h. This system exhibits an active phase when p is smaller than a critical value, p c . For p ≥ p c the system evolves into a frozen (absorbing) state where the nearest-neighbor pairs are absent. Further details of the model can be found in Ref. [5]. This extended model was studied by Monte Carlo (MC) simulations and dynamical cluster mean-field approximation for quite large cluster sizes (ranged from n = 2 to 6). Some disturbing behaviors, however, remained unsolved. For example, the analytical predictions tend not monotonously toward the MC results for h > 0 when the cluster size is increased. Furthermore the analytical results shows a discontinuity in the variation of critical point p c if h → 0. This observation is surprising because the present approximation has proved to be satisfactory in many cases for n ≤ 6 [6]. It is expected that the further increase of cluster size will resolve these discrepancies.In this Brief Report, we discuss the results of dynamical mean-field approximations for cluster sizes as large as n = 12. The present a...

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Scaling behavior of the directed percolation universality class

Lübeck

Willmann

2005

Nuclear Physics B

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In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling behavior, we present clear numerical evidence that all models belong to the universality class of directed percolation. Since the considered models are characterized by different interaction details the obtained universal scaling plots are an impressive manifestation of the universality of directed percolation.Comment: 24 pages, 7 figures, accepted for publication in Nuclear Physics

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Pair contact process with a particle source

Cited by 19 publications

References 42 publications

Conserved Sandpile with A Variable Height Restriction

Conserved Sandpile with A Variable Height Restriction

Dynamical mean-field approximation for a pair contact process with a particle source

Scaling behavior of the directed percolation universality class

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