Zeitschrift für Physik B Condensed Matter

, Volume 63, Issue 4, pp 521–535 | Cite as

Fluctuations and lack of self-averaging in the kinetics of domain growth

  • A. Milchev
  • K. Binder
  • D. W. Heermann


The fluctuations occurring when an initially disordered system is quenched at timet=0 to a state, where in equilibrium it is ordered, are studied with a scaling theory. Both the mean-sizel(t)d of thed-dimensional ordered domains and their fluctuations in size are found to increase with the same power of the time; their relative size fluctuations are independent of the total volumeLd of the system. This lack of self-averaging is tested for both the Ising model and the φ4 model on the square lattice. Both models exhibit the same lawl(t)=(Rt)x withx=1/2, although the φ4 model has “soft walls”. However, spurious results withx≷1/2 are obtained if “bad” pseudorandom numbers are used, and if the numbern of independent runs is too small (n itself should be of the order of 103). We also predict a critical singularity of the rateR∝(1−T/Tc)v(z−1/x),v being the correlation length exponent,z the dynamic exponent.

Also quenches to the critical temperatureTc itself are considered, and a related lack of self-averaging in equilibrium computer simulations is pointed out for quantities sampled from thermodynamic fluctuation relations.


Neural Network Computer Simulation Nonlinear Dynamics Relative Size Correlation Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • A. Milchev
    • 1
  • K. Binder
    • 1
  • D. W. Heermann
    • 1
  1. 1.Institut für PhysikJohannes Gutenberg-Universität MainzMainzGermany

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