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

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Abstract

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. Coherent anomaly analysis of the data supports the conclusion that the vanishing of the order parameter and the density of isolated particles have 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.

Original languageEnglish
Article number057102
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume66
Issue number5
DOIs
Publication statusPublished - Nov 2002

Fingerprint

Contact Process
Mean-field Approximation
Critical Behavior
approximation
Approximation
Extrapolation
Order Parameter
Anomaly
extrapolation
Vanish
Discontinuity
Critical point
critical point
discontinuity
anomalies
Prediction
Zero
predictions

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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AB - 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. Coherent anomaly analysis of the data supports the conclusion that the vanishing of the order parameter and the density of isolated particles have 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.

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