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Aging, phase ordering, and conformal invariance.

M Henkel1, M Pleimling, C Godrèche

  • 1Laboratoire de Physique des Matériaux, Université Henri Poincaré Nancy I, BP 239, F-54506 Vandoeuvre lès Nancy Cedex, France.

Physical Review Letters
|January 22, 2002
PubMed
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This study extends dynamical scaling to conformal invariance, revealing the explicit form of the scaling function for aging systems. This finding is validated across various spin models, including critical dynamics and phase ordering.

Area of Science:

  • Statistical physics
  • Condensed matter physics
  • Dynamical systems

Background:

  • Aging phenomena in physical systems often exhibit two-time response function scaling.
  • Understanding the universal behavior of these systems is crucial for theoretical advancements.

Purpose of the Study:

  • To extend dynamical scaling to conformal invariance.
  • To derive the explicit form of the scaling function for aging systems.
  • To validate theoretical predictions with numerical and exact results.

Main Methods:

  • Theoretical analysis connecting dynamical scaling to conformal invariance.
  • Numerical simulations of the 2D and 3D Ising models with Glauber dynamics.
  • Exact solutions for the spherical model with nonconserved order parameter.

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Main Results:

  • The explicit form of the scaling function f(t/s) was derived.
  • The theoretical predictions were confirmed in various spin systems.
  • Results cover both phase ordering (T

Conclusions:

  • Dynamical scaling can be unified with conformal invariance.
  • The derived scaling function provides a quantitative description of aging dynamics.
  • The findings are robust across different models and interaction ranges.