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Persistence in systems with algebraic interaction.

I Ispolatov1

  • 1Department of Physics, McGill University, 3600 rue University, Montréal, Québec, Canada H3A 2T8.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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Persistence in one-dimensional spin systems with power-law interactions decays algebraically for large exponents (sigma >= 1/2). The persistence exponent (theta) is independent of sigma, matching the extremal model. Finite size effects impact smaller exponents.

Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Investigates coarsening dynamics in one-dimensional spin systems.
  • Focuses on systems with power-law interactions of the form r(-1-sigma).

Purpose of the Study:

  • To determine the persistence behavior in one-dimensional spin systems with power-law interactions.
  • To analyze the influence of the interaction exponent (sigma) on persistence decay.
  • To identify the persistence exponent (theta) and its relation to sigma.

Main Methods:

  • Employs numerical studies to simulate spin system dynamics.
  • Analyzes the algebraic decay of persistence P(L) as a function of length scale L.
  • Utilizes scaling arguments to understand finite size effects and boundary conditions.

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Main Results:

  • For sigma >= 1/2, persistence decays algebraically: P(L) approximately L(-theta).
  • The persistence exponent theta is approximately 0.17507588, independent of sigma.
  • For sigma < 1/2, finite size effects hinder reaching the asymptotic regime.

Conclusions:

  • Persistence exponent is constant for sufficiently large interaction exponents (sigma).
  • System size must scale as [O(1/sigma)](1/sigma) to mitigate boundary effects for small sigma.
  • The study provides insights into critical phenomena and scaling laws in disordered systems.