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Slow relaxation in the large-N model for phase ordering.

Federico Corberi1, Eugenio Lippiello, Marco Zannetti

  • 1Istituto Nazionale per la Fisica della Materia, Unità di Salerno and Dipartimento di Fisica, E. Caianiello, Università di Salerno, 84081 Baronissi, Salerno, Italy. corberi@na.infn.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2002
PubMed
Summary

This study analytically investigates slow relaxation in phase ordering processes using the large-N model. It reveals how dimensionality affects the aging response function, showing critical behavior at d=4.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Phase ordering processes exhibit slow relaxation dynamics.
  • Understanding the aging contribution to response functions is crucial for characterizing these dynamics.

Purpose of the Study:

  • To analytically derive the slow relaxation phenomenology in the large-N model.
  • To investigate the dimensionality dependence of the aging contribution to the response function.

Main Methods:

  • Exact separation of the order parameter into thermal and condensation components.
  • Analysis of the aging contribution to the response function chi(ag)(t,t(w)) in the large-N model.

Main Results:

  • The aging contribution exhibits behavior similar to Ising systems when dimensionality is varied.

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  • A critical dimensionality (d=4) is identified, above which chi(ag)(t,t(w)) scales with defect density.
  • For d<4, chi(ag)(t,t(w)) vanishes slower than defect density, and at d=2, it does not vanish.

    • Conclusions:

    • The dimensionality dependence of the interplay between defect density and single-defect response explains the observed behavior.
    • The large-N model provides an analytical framework to understand complex relaxation phenomena in physical systems.