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Correlation functions in the two-dimensional random-field Ising model.

S L de Queiroz1, R B Stinchcombe

  • 1Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, Campus da Praia Vermelha, 24210-340 Niterói RJ, Brazil. sldq@if.ufrj.br

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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This study investigates spin-spin correlation functions in the 2D random-field Ising model. Numerical and analytical methods reveal how field fluctuations and temperature influence these correlations, particularly near critical points.

Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Computational physics

Background:

  • The random-field Ising model is crucial for understanding disordered magnetic systems.
  • Spin-spin correlation functions characterize the magnetic ordering and fluctuations within materials.
  • Previous studies often focused on idealized conditions, necessitating investigation under more realistic random field distributions.

Purpose of the Study:

  • To analyze the probability distributions of spin-spin correlation functions (G) in the 2D random-field Ising model.
  • To explore the impact of temperature (T), field intensity (h(0)), and system width (L) on these distributions.
  • To establish connections between correlation function distributions and underlying field fluctuations.

Main Methods:

Related Experiment Videos

  • Transfer-matrix methods were employed to study long strips of varying widths (L=3-15 sites).
  • Binary field distributions were used to simulate realistic random field conditions.
  • Numerical simulations were complemented by analytical expressions for validation.

    • Main Results:

    • For moderate temperatures and experimental field strengths, correlation distributions are singly peaked but asymmetric.
    • At low temperatures, distributions transition towards a double-delta structure, indicating ground-state behavior.
    • A scaling relation for averaged correlation functions with L(y)h(0) was predicted and numerically confirmed (y ≈ 0.875).
    • The root-mean-square relative width (W) of distributions shows dependence on field intensity and system size.

    Conclusions:

    • The study provides insights into the complex behavior of correlation functions in disordered magnetic systems.
    • The findings bridge theoretical predictions with numerical observations, particularly concerning critical scaling.
    • The results offer a more nuanced understanding of magnetic properties under random fields, relevant for experimental interpretation.