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Related Experiment Videos

Spin models with random anisotropy and reflection symmetry.

Pasquale Calabrese1, Andrea Pelissetto, Ettore Vicari

  • 1Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, I-56126 Pisa, Italy. calabres@df.unipi.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
PubMed
Summary

This study demonstrates that disordered cubic-symmetric spin systems exhibit critical behavior belonging to the random-exchange Ising universality class. This finding is supported by renormalization-group analysis, confirming a stable fixed point for these systems.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Disordered Systems

Background:

  • Cubic-symmetric spin systems are fundamental models in statistical mechanics.
  • Understanding critical behavior in disordered systems is crucial for materials science.
  • Disorder can significantly alter the phase transitions of magnetic systems.

Purpose of the Study:

  • To investigate the critical behavior of general cubic-symmetric spin systems with specific disorder properties.
  • To determine the universality class of these systems under symmetry-preserving disorder.
  • To analyze the renormalization-group flow and identify stable fixed points.

Main Methods:

  • Application of nonperturbative arguments to identify stable fixed points.
  • Field-theoretical renormalization-group (RG) analysis.

Related Experiment Videos

  • Fixed-dimension expansion in quartic couplings, calculating beta functions to five loops.

    • Main Results:

    • Demonstrated the existence of a stable fixed point corresponding to the random-exchange Ising universality class.
    • Showed that the random Ising fixed point is the sole accessible stable fixed point from the relevant parameter region.
    • Identified scaling corrections to critical behavior with exponent Delta = -alpha(r), where alpha(r) is the specific-heat exponent.

    Conclusions:

    • Disordered cubic-symmetric spin systems with reflection symmetry belong to the random-exchange Ising universality class.
    • The identified fixed point governs the asymptotic critical behavior.
    • Scaling corrections provide insight into the approach to this critical behavior.