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Correlated disordered interactions on Potts models.

P T Muzy1, A P Vieira, S R Salinas

  • 1Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970 São Paulo, Sao Paulo, Brazil. ptmuzy@uol.com.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2002
PubMed
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This study analyzes critical behavior in q-state Potts models with correlated disorder on hierarchical lattices. Results reveal distinct behaviors based on dimensionality, differentiating between non-perturbative and perturbative fixed points.

Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Phase transitions

Background:

  • The study of disordered systems is crucial for understanding complex materials.
  • Correlated disorder in magnetic systems presents unique theoretical challenges.
  • Previous numerical work by Andelman and Aharony (1985) established a baseline for comparison.

Purpose of the Study:

  • To derive analytical results for critical behavior in q-state Potts models with correlated disorder.
  • To investigate the influence of dimensionality on the system's behavior.
  • To generalize the Harris criterion for correlated disorder relevance.

Main Methods:

  • Application of a weak-disorder scheme.
  • Utilization of real-space renormalization-group techniques.

Related Experiment Videos

  • Analysis on hierarchical (Migdal-Kadanoff) lattices.

    • Main Results:

    • Analytical results obtained for critical behavior of q-state Potts models.
    • Qualitative differences observed between d-d(1)=1 and d-d(1)>1 cases.
    • Identification of non-physical random fixed points for d-d(1)=1, suggesting non-perturbative fixed distributions.
    • Identification of acceptable perturbative random fixed points for d-d(1)>1.
    • Re-derivation of a generalized criterion for correlated disorder relevance.

    Conclusions:

    • The dimensionality of correlated disorder significantly impacts critical behavior.
    • Findings align with and extend previous numerical studies.
    • The generalized criterion offers a new perspective on disorder relevance in statistical models.