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Disorder averaging and finite-size scaling

Bernardet1, Pazmandi, Batrouni

  • 1Institut Non-Lineaire de Nice, Universite de Nice-Sophia Antipolis, 1361 route des Lucioles, 06560 Valbonne, France.

Physical Review Letters
|September 16, 2000
PubMed
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This study introduces a new renormalization group (RG) approach for disordered systems, averaging randomness after finding critical points. This method resolves finite-size corrections observed in the 2D random-bond Ising model.

Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Disordered systems present challenges for traditional renormalization group (RG) methods.
  • Existing RG approaches often renormalize averaged free energy, obscuring system-specific critical behavior.

Purpose of the Study:

  • To propose a novel RG framework that accounts for disorder by analyzing individual random samples.
  • To investigate the impact of this new approach on finite-size scaling in disordered systems.

Main Methods:

  • Developed a new renormalization group (RG) picture considering individual random sample trajectories.
  • Applied the new RG approach to study the finite-size scaling of the 2D random-bond Ising model.
  • Compared results with traditional RG methods based on averaged free energy.

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Main Results:

  • Demonstrated that averaging over randomness should occur after determining the critical point for each realization.
  • Identified sample-to-sample fluctuations in critical temperature as the cause of previously observed finite-size corrections.
  • Showed that scaling predictions are accurately fulfilled only by the new averaging method.

Conclusions:

  • The proposed RG approach provides a more accurate description of critical phenomena in disordered systems.
  • This method correctly accounts for sample-to-sample fluctuations, leading to improved finite-size scaling predictions.
  • The findings necessitate a re-evaluation of established RG techniques for disordered materials.