Critical decay exponent of the pair contact process with diffusion

Park, Su‐Chan

doi:10.1103/physreve.90.052115

Cited by 16 publications

(20 citation statements)

References 34 publications

(84 reference statements)

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“…In the physics literature, considerable attention has been paid to the "pair contact process" where again the reproduction mechanisms is cooperative branching, but the death mechanism is annihilation (two particles are simultaneously removed). Whether this model belongs to the directed percolation (DP) universality class is the subject of ongoing debate [24,25].…”

Section: Resultsmentioning

confidence: 99%

A particle system with cooperative branching and coalescence

Sturm¹,

Swart²

2015

Ann. Appl. Probab.

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In this paper, we introduce a one-dimensional model of particles performing independent random walks, where only pairs of particles can produce offspring ("cooperative branching"), and particles that land on an occupied site merge with the particle present on that site ("coalescence"). We show that the system undergoes a phase transition as the branching rate is increased. For small branching rates, the upper invariant law is trivial, and the process started with finitely many particles a.s. ends up with a single particle. Both statements are not true for high branching rates. An interesting feature of the process is that the spectral gap is zero even for low branching rates. Indeed, if the branching rate is small enough, then we show that for the process started in the fully occupied state, the particle density decays as one over the square root of time, and the same is true for the decay of the probability that the process still has more than one particle at a later time if it started with two particles.Comment: Published at http://dx.doi.org/10.1214/14-AAP1032 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Section: Resultsmentioning

confidence: 99%

A particle system with cooperative branching and coalescence

Sturm¹,

Swart²

2015

Ann. Appl. Probab.

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“…Since Q m is measured at the disordered phase, the curves should eventually veer down [23] as can be seen at the tail of the curves in the inset. Still, the power-law region is observable and we conclude that the CSE is about 0.75.…”

Section: Interacting Monomer-dimer Modelmentioning

confidence: 96%

“…To this end, we use the method introduced recently [22,23]. We numerically calculate the corrections-to-scaling functions (CTSFs)…”

Section: Preliminary : Dynamic Exponent Of the Two Dimensional Ising mentioning

confidence: 99%

Order–disorder transition in the two-dimensional interacting monomer-dimer model: Ising criticality

Park¹

2015

J. Stat. Mech.

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Abstract. We study the order-disorder transition of the two dimensional interacting monomer-dimer model (IMD) which has two symmetric absorbing states. To be selfcontained, we first estimate numerically the dynamic exponent z of the two dimensional Ising model. From the relaxation dynamics of the magnetization at the critical point, we obtain β/(νz) = 0.057 650(12), or z = 2.168 26(45), where β = 1 8 and ν = 1 are exactly known exponents. We, then, compare the critical relaxation of the order parameter at the transition point of the IMD with that of the Ising model. We found that the critical relaxation exponent β/(νz) is in good agreement with the Ising model, unlike the recent claim by Nam et al [JSTAT (2014), P08011]. We also claim that the Binder cumulant is not an efficient quantity to locate the order-disorder transition point of the model with two symmetric absorbing states.

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“…[14], which is larger than the more accurate estimate in Ref. [23], one should note that the accuracy of p 0 in Ref. [14] was attained without resorting much to the accuracy of α; the critical point was actually estimated by finding two p's belonging to the absorbing and active phases, respectively.…”

Section: Resultsmentioning

confidence: 98%

“…In one theory, the PCPD is claimed to form a different universality class from the directed percolation (DP) universality class [10,14,15,17,20,23]. This theory is supported by the following facts: First, the upper critical dimension of the PCPD is 2 [26], while that of the DP is 4.…”

Section: Introductionmentioning

confidence: 99%

Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion

Park

2017

Phys. Rev. E

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The one-dimensional pair contact process with diffusion (PCPD), an interacting particle system with diffusion, pair annihilation, and creation by pairs, has defied consensus about the universality class to which it belongs. An argument by Hinrichsen [Physica A 361, 457 (2006)PHYADX0378-437110.1016/j.physa.2005.06.101] claims that freely diffusing particles in the PCPD should play the same role as frozen particles when it comes to the critical behavior. Therefore, the PCPD is claimed to have the same critical phenomena as a model with infinitely many absorbing states that belongs to the directed percolation (DP) universality class. To investigate if diffusing particles are really indistinguishable from frozen particles in the sense of the renormalization group, we study numerically a variation of the PCPD by introducing a nonorder field associated with infinitely many absorbing states. We find that a crossover from the PCPD to DP occurs due to the nonorder field. By studying a similar model, we exclude the possibility that the mere introduction of a nonorder field to one model can entail a nontrivial crossover to another model in the same universality class, thus we attribute the observed crossover to the difference of the universality class of the PCPD from the DP class.

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Critical decay exponent of the pair contact process with diffusion

Cited by 16 publications

References 34 publications

A particle system with cooperative branching and coalescence

A particle system with cooperative branching and coalescence

Order–disorder transition in the two-dimensional interacting monomer-dimer model: Ising criticality

Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion

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