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Moment ratios for the pair-contact process with diffusion.

Marcelo M de Oliveira1, Ronald Dickman

  • 1Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, C. P. 702, 30123-970, Belo Horizonte, Minas Gerais-Brazil. mancebo@fisica.ufmg.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 16, 2006
PubMed
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This study investigates the continuous absorbing-state phase transition in the one-dimensional pair contact process with diffusion (PCPD). New simulations reveal that finite-size effects cause anomalous moment ratios, which converge to universal values only in large systems.

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Phase Transitions

Background:

  • The one-dimensional pair contact process with diffusion (PCPD) exhibits a continuous absorbing-state phase transition.
  • Previous studies reported anomalous behavior in order parameter moment ratios at the critical point, which did not converge to universal values with increasing system size.

Purpose of the Study:

  • To accurately determine the critical point moment ratios of the order parameter in the PCPD model.
  • To investigate the influence of finite-size effects on these ratios.
  • To compare the PCPD critical behavior with that of directed percolation.

Main Methods:

  • Utilized the quasistationary simulation method to analyze the PCPD model.
  • Simulated systems up to 40,960 sites to capture finite-size effects.

Related Experiment Videos

  • Calculated order parameter moments up to the fourth order at the critical point.

    • Main Results:

    • Observed that order parameter moment ratios exhibit anomalous behavior due to strong finite-size effects.
    • Demonstrated that these ratios converge to universal values only for sufficiently large system sizes.
    • Provided an improved estimate for the critical point of the nondiffusive pair contact process: pc=0.077092(1).

    Conclusions:

    • Finite-size effects are crucial for understanding the critical behavior of the PCPD.
    • The PCPD shares similarities with directed percolation in its critical behavior, as indicated by moment ratio and histogram comparisons.
    • Accurate determination of critical parameters requires careful consideration of system size in simulations.