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Surface critical behavior in systems with nonequilibrium phase transitions

Howard1, Frojdh, Baekgaard Lauritsen K

  • 1Department of Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
Summary

We investigated surface critical behavior in branching-annihilating random walks (BARW) and directed percolation (DP). BARW models exhibit distinct phase diagrams and unique surface exponents in lower dimensions, confirmed by simulations.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems

Background:

  • Branching-annihilating random walks (BARW) and directed percolation (DP) are fundamental models in statistical physics.
  • Understanding their surface critical behavior is crucial for various phenomena.

Purpose of the Study:

  • To analyze the surface critical behavior of BARW and DP.
  • To compare mean-field predictions with fluctuation effects in lower dimensions.

Main Methods:

  • Mean-field theory for dimensions above the upper critical dimension.
  • Field-theoretic methods for dimensions at or below the upper critical dimension.
  • Exact duality transformation for lattice BARW models in d=1.

Main Results:

  • Surface phase diagrams for DP and BARW were analyzed.

Related Experiment Videos

  • BARW phase diagrams in d=1 and d=2 differ significantly from mean-field predictions.
  • Two independent surface beta(1) exponents were identified for BARW in d=1.
  • A relationship between these exponents was uncovered.

    • Conclusions:

    • Fluctuations significantly alter BARW surface behavior in lower dimensions.
    • The findings highlight the complexity of BARW universality classes.
    • Monte Carlo simulations support the theoretical predictions.