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Related Experiment Videos

Ground state nonuniversality in the random-field Ising model.

P M Duxbury1, J H Meinke

  • 1Department of Physics and Astronomy and Center for Fundamental Materials Research, Michigan State University, East Lansing, Michigan 48824, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
Summary

Universality and zero-temperature fixed points are violated in random-field Ising models. Disorder affects ground state exponents, but temperature restores universal behavior at finite temperatures.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Disordered systems

Background:

  • Universality is a key concept in statistical mechanics, describing systems that share critical behavior regardless of microscopic details.
  • Zero-temperature fixed points are crucial for understanding the ground states of many physical systems.
  • The random-field Ising model is a fundamental model for studying disorder effects in magnetic systems.

Purpose of the Study:

  • To investigate the validity of universality and zero-temperature fixed points in the infinite-range random-field Ising model.
  • To determine the behavior of critical exponents in the presence of disorder.
  • To analyze the role of temperature as a relevant variable.

Main Methods:

  • Theoretical analysis of the infinite-range random-field Ising model.

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  • Investigation of the ground state properties.
  • Examination of thermal behavior at finite temperatures.

    • Main Results:

    • Universality and the zero-temperature fixed point concept are violated in this model.
    • Ground state critical exponents exhibit continuous dependence on disorder, indicating nonuniversality.
    • At finite temperatures, the thermal order-parameter exponent of 1/2 is restored, confirming temperature's relevance.

    Conclusions:

    • The infinite-range random-field Ising model deviates from standard universality predictions.
    • Disorder plays a significant role in determining ground state properties, leading to nonuniversal behavior.
    • Temperature acts as a relevant variable, restoring universal scaling at finite temperatures.