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Related Experiment Videos

Complexity of vector spin glasses.

J Yeo1, M A Moore

  • 1Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.

Physical Review Letters
|August 25, 2004
PubMed
Summary
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We analyzed the annealed complexity of m-vector spin glasses. The study reveals a surprising eigenvalue spectrum, indicating supersymmetry breaking similar to Ising spin glasses.

Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Spin glass theory

Background:

  • The Sherrington-Kirkpatrick (SK) model is a fundamental model for spin glasses.
  • Understanding the complexity and phase transitions in spin glasses is crucial for theoretical physics.

Purpose of the Study:

  • To investigate the annealed complexity of m-vector spin glasses within the Sherrington-Kirkpatrick limit.
  • To analyze the eigenvalue spectrum of the Hessian matrix of the Thouless-Anderson-Palmer (TAP) free energy.

Main Methods:

  • Analysis of the eigenvalue spectrum of the Hessian matrix of the TAP free energy.
  • Examination of the behavior of eigenvalues at finite temperatures and in the thermodynamic limit.

Main Results:

Related Experiment Videos

  • The eigenvalue spectrum comprises a continuous band of positive eigenvalues, an isolated eigenvalue, and (m-1) null eigenvalues due to rotational invariance.
  • The continuous band of eigenvalues does not reach zero at any finite temperature.
  • The isolated eigenvalue tends to zero in the thermodynamic limit.

Conclusions:

  • The findings indicate that supersymmetry breaking, previously observed in Ising spin glasses (m=1), also occurs in m-vector spin glasses.
  • This suggests a universal mechanism for supersymmetry breaking across different spin glass models.