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Related Experiment Videos

Finite-size scaling in disordered systems.

H Chamati1, E Korutcheva, N S Tonchev

  • 1G. Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
Summary

This study analyzes critical behavior in quenched random systems using renormalization group methods. Finite-size scaling and self-averaging properties are clarified near the upper critical dimension.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Quantum Field Theory

Background:

  • Understanding critical phenomena in disordered systems is crucial for materials science.
  • The
  • random-T(c)
  • model provides a framework for studying quenched disorder effects.

Purpose of the Study:

  • To investigate the critical behavior of quenched random hypercubic systems.
  • To analyze finite-size scaling and self-averaging properties near the upper critical dimension.

Main Methods:

  • Renormalization group (RG) method applied to a quenched random hypercubic sample.
  • Analysis of finite-size scaling behavior near d=4-epsilon.
  • Clarification of self-averaging for various critical regimes.

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Main Results:

  • Establishment and analysis of finite-size scaling behavior.
  • Obtained universal results near the upper critical dimension.
  • Clarified the problem of self-averaging in different critical regimes.

Conclusions:

  • The study provides insights into the critical behavior of disordered systems.
  • Finite-size scaling and self-averaging are key aspects near the upper critical dimension.
  • Universal results obtained contribute to the understanding of statistical mechanics models.