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Interface scaling in the contact process

Dickman1, Munoz

  • 1Departamento de Fisica, ICEx, Universidade Federal de Minas Gerais, 30161-970 Belo Horizonte, MG, Brazil.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|January 4, 2001
PubMed
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This study links absorbing state models to pinned interfaces using height variables. Simulations confirm a key scaling relation between interface width and order parameter decay in 1-3 dimensions.

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Condensed Matter Physics

Background:

  • A known correspondence exists between lattice models with absorbing states and pinned interfaces in random media.
  • Local height variables, defined as integrals of activity, facilitate studying this interface representation.
  • The contact process is a prototypical model with absorbing states relevant to this research.

Purpose of the Study:

  • To investigate the interface representation of the contact process in dimensions 1-3.
  • To confirm the scaling relation between interface width growth and order parameter decay.
  • To analyze the scaling properties of height distributions and height-height correlations.

Main Methods:

  • Defining local height variables h(x,t) as integrals of activity.

Related Experiment Videos

  • Simulating the contact process in 1, 2, and 3 dimensions.
  • Analyzing interface width growth, order parameter decay, height distributions, and height-height correlations.

    • Main Results:

    • Simulations confirmed the scaling relation beta(W) = 1 - theta.
    • A specific scaling property of the height distribution was verified.
    • Height-height correlation functions exhibited anomalous scaling, consistent with prior work.

    Conclusions:

    • The study validates the established correspondence between absorbing state models and pinned interfaces.
    • The findings support the universality of the observed scaling relations in these systems.
    • Anomalous scaling in height correlations was observed, but multiscaling was not detected.