Anomalous Diffusion in Non-Equilibrium Systems

  • E. Arapaki
  • P. Argyrakis
  • M. C. Tringides
Part of the NATO ASI Series book series (NSSB, volume 360)


We study the tracer diffusion in the 2-dimensional Ising model with attractive interaction J under non-equilibrium conditions. We calculate < R 2 >, the mean square displacement averaged over all the particles for different \(\frac{J}{{kT}}\) ratios where J is the nearest-neighbor coupling constant and T the temperature. The system shows sublinear dependence on time < R 2 >~ t 1–x for ratios below the transition temperature \((\frac{J}{{kT}} > 1.88)\) into the ordered (1×1) phase and for early enough times. The sublinearity can be related to the evolution of the ordered domains. For sufficiently long times linear dependence is observed which signifies that one effective barrier is attained. We determine the transition times t c (T) where the crossover to the linear time dependence occurs. In addition, we calculate the time dependent jumping rate W(t) for different ratios \(\frac{J}{{kT}}\) . For ratios within the ordered region W(t) shows a power law decay W(t) ~ t x with the exponent x′ linearly related to the exponent describing the time dependence of < R 2 >.


Effective Activation Energy Tracer Diffusion Domain Growth Random Configuration Crossover Time 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • E. Arapaki
    • 1
  • P. Argyrakis
    • 1
  • M. C. Tringides
    • 2
  1. 1.Department of PhysicsUniversity of ThessalonikiThessalonikiGreece
  2. 2.Ames Laboratory and Department of Physics and AstronomyIowa State UniversityAmesUSA

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