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Stochastic processes and conformal invariance.

Jan de Gier1, Bernard Nienhuis, Paul A Pearce

  • 1Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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This study models fluctuating interfaces using a dynamic exponent of 1. It reveals a connection between logarithmic conformal field theory and stochastic processes, with new critical exponents for avalanche sizes.

Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Theoretical Physics

Background:

  • Fluctuating interfaces are crucial in various physical phenomena.
  • Understanding their dynamics requires advanced theoretical frameworks.
  • Previous models often simplified complex interactions.

Purpose of the Study:

  • To develop a one-dimensional model for fluctuating interfaces.
  • To explore the connection between logarithmic conformal field theory and stochastic processes.
  • To analyze avalanche phenomena during desorption.

Main Methods:

  • Development of a one-dimensional fluctuating interface model.
  • Analysis using concepts from c=0 logarithmic conformal field theory.
  • Investigation of finite-size scaling behavior and avalanche distributions.

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Main Results:

  • Established a rigorous link between logarithmic conformal field theory and stochastic processes.
  • Characterized the time dependence in the thermodynamic limit.
  • Identified finite-size scaling for interface properties and new critical exponents for avalanche sizes.

Conclusions:

  • The model provides a rigorous framework for studying interface dynamics.
  • Logarithmic conformal field theory offers insights into stochastic processes.
  • Avalanche analysis reveals novel scaling behaviors in finite systems.