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Perturbation expansion in phase-ordering kinetics. II. N-vector model

Mazenko1

  • 1The James Franck Institute and the Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
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This study generalizes phase-ordering kinetics theory for nonconserved order parameters to the n-vector model. Second-order corrections to nonequilibrium exponents were calculated, showing corrections vanish in large n and d limits.

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Non-equilibrium Systems

Background:

  • Phase-ordering kinetics describes how systems with multiple degenerate ground states evolve over time.
  • Previous work established a perturbation theory for scalar order parameters.
  • The n-vector model is a generalization with n components, relevant to diverse physical systems.

Purpose of the Study:

  • To generalize the perturbation theory for phase-ordering kinetics to the n-vector model.
  • To calculate second-order corrections to nonequilibrium exponents.
  • To analyze the behavior of these corrections in various limits.

Main Methods:

  • Perturbation theory expansion applied to the n-vector model.
  • Explicit calculation of second-order corrections to nonequilibrium exponents.

Related Experiment Videos

  • Analysis of results in d dimensions and as a function of n components.

    • Main Results:

    • The lowest order of the expansion reproduces the Ohta-Jasnow-Kawasaki (OJK) theory.
    • Second-order corrections to nonequilibrium exponents were derived.
    • These corrections were found to diminish in the large n and large d limits.

    Conclusions:

    • The generalized theory provides a framework for studying phase-ordering in n-vector models.
    • The OJK theory is a robust approximation in the large n and large d limits.
    • Large-d convergence is shown to be exponential, indicating rapid stabilization.