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

Attila Szolnoki1

  • 1Research Institute for Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary. szolnoki@mfa.kfki.hu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 7, 2003
PubMed
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This study investigates the one-dimensional pair contact process with a particle source. Reliable extrapolations suggest critical behavior in the order parameter and isolated particle density, differing from prior predictions.

Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • The one-dimensional pair contact process is a fundamental model for studying spreading phenomena.
  • Understanding the influence of particle sources on system dynamics is crucial for complex systems research.

Purpose of the Study:

  • To investigate the behavior of the one-dimensional pair contact process with a particle source.
  • To determine the critical behavior and phase transitions in this system using advanced approximation methods.

Main Methods:

  • Dynamical cluster mean-field approximations were employed with system sizes up to n=12.
  • Coherent anomaly analysis was used to analyze critical phenomena.
  • Extrapolation to the thermodynamic limit (n --> infinity) was performed.

Main Results:

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  • Results converged for approximations with n>=6, enabling reliable extrapolations.
  • A discontinuity at the critical point was observed in the zero source limit, vanishing as 1/n.
  • The order parameter and isolated particle density exhibit the same critical behavior.

Conclusions:

  • The study provides reliable extrapolations for the one-dimensional pair contact process with a particle source.
  • The findings challenge earlier predictions regarding critical behavior in the inactive phase.
  • The research clarifies the critical dynamics of particle density and order parameter vanishing.