Critical properties of the reaction-diffusion model<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mn>3</mml:mn><mml:mi>A</mml:mi><mml:mo>,</mml:mo></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>A</mml:mi></mml:mro

Carlon, Enrico; Henkel, Malte; Schollwöck, Ulrich

doi:10.1103/physreve.63.036101

Cited by 98 publications

(197 citation statements)

References 56 publications

Supporting

Mentioning

179

Contrasting

Order By: Relevance

“…At the PCPD point (r = 1), our results are consistent with those obtained by Carlon et al [34] (p c = 0.111(2), z = 1.87(3), β/ν ⊥ = 0.50(3)) and Hinrichsen [35] (p c = 0.1112(1), β/ν = 0.25(2), z = 1.83(5), β < 0.67). Although some of critical exponent ratios are close to the DI values, the critical exponents are incompatible with those of the DI class.…”

Section: B Static Simulationssupporting

confidence: 93%

Universality class of absorbing transitions with continuously varying critical exponents

Noh

Park

2004

Phys. Rev. E

View full text Add to dashboard Cite

The well-established universality classes of absorbing critical phenomena are directed percolation (DP) and directed Ising (DI) classes. Recently, the pair contact process with diffusion (PCPD) has been investigated extensively and claimed to exhibit a new type of critical phenomena distinct from both DP and DI classes. Noticing that the PCPD possesses a long-term memory effect, we introduce a generalized version of the PCPD (GPCPD) with a parameter controlling the memory effect. The GPCPD connects the DP fixed point to the PCPD point continuously. Monte Carlo simulations show that the GPCPD displays novel type critical phenomena which are characterized by continuously varying critical exponents. The same critical behaviors are also observed in models where two species of particles are coupled cyclically. We suggest that the long-term memory may serve as a marginal perturbation to the ordinary DP fixed point.

show abstract

Section: B Static Simulationssupporting

confidence: 93%

Universality class of absorbing transitions with continuously varying critical exponents

Noh

Park

2004

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…Its preliminary simulations in 1d showed a non-DP type transition, but these results have been forgotten for a long time. The diffusive pair contact process (PCPD) introduced by Carlon et al [14] is controlled by two independent parameters: the probability of pair annihilation p and the probability of particle diffusion D. The dynamical rules are…”

Section: The Pcpd Modelmentioning

confidence: 99%

Critical behavior of the one-dimensional diffusive pair contact process

Ódor

2003

Phys. Rev. E

View full text Add to dashboard Cite

The phase transition of the one-dimensional, diffusive pair contact process (PCPD) is investigated by N cluster mean-field approximations and high precision simulations. The N = 3, 4 cluster approximations exhibit smooth transition line to absorbing state by varying the diffusion rate D with β2 = 2 mean-field order parameter exponent of the pair density. This contradicts with former N = 2 results, where two different mean-field behavior was found along the transition line. Extensive dynamical simulations on L = 10 5 lattices give estimates for the order parameter exponents of the particles for 0.05 ≤ D ≤ 0.7. These data can support former two distinct class findings. However the gap between low and high D exponents is narrower than estimated previously and the possibility for interpreting numerical data as a single class behavior with exponents α = 0.21(1), β = 0.41(1) assuming logarithmic corrections is shown. Finite size scaling and cluster simulation results are also presented.

show abstract

“…Mean-field-like kinetic equations for the PCPD were obtained in [6]. Whereas the single-site approximation is only appropriate to the high diffusion limit (D → 1), the pair approximation gives a good qualitative picture of the model for D > 0, but does not show some important characteristics of the PCP without diffusion.…”

Section: Cluster Approximationmentioning

confidence: 99%

Static critical behavior in the inactive phase of the pair contact process

2001

View full text Add to dashboard Cite

Steady state properties in the absorbing phase of the 1d pair contact process (PCP) model are investigated. It is shown that, in typical absorbing states (reached by the system's dynamic rules), the density of isolated particles, ρ1, approaches a stationary value which depends on the annihilation probability (p); the deviation from its 'natural' value at criticality, ρ nat 1 , follows a power law: ρ nat 1 − ρ1 ∼ (p − pc) β 1 for p > pc. Monte Carlo simulations yield β1 = 0.81. A cluster approximation is developed for this model, qualitatively confirming the numerical results and predicting β1 = 1. The singular behavior of the isolated particles density in the inactive phase is explained using a phenomenological approach.

show abstract

Critical properties of the reaction-diffusion model2A→3A,2A

Cited by 98 publications

References 56 publications

Universality class of absorbing transitions with continuously varying critical exponents

Universality class of absorbing transitions with continuously varying critical exponents

Critical behavior of the one-dimensional diffusive pair contact process

Static critical behavior in the inactive phase of the pair contact process

Contact Info

Product

Resources

About