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R R P Singh1, A P Young2

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This summary is machine-generated.

High-temperature series expansions reveal scaling dimension Δ=2 in spin glasses for dimensions d≥6 and the infinite-range Sherrington-Kirkpatrick model. Anomalous de Almeida-Thouless line behavior occurs in finite fields at high dimensions.

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Disordered systems

Background:

  • Spin glasses exhibit complex magnetic behavior due to quenched disorder.
  • Understanding the influence of magnetic fields on spin glass phase transitions is crucial.
  • The de Almeida-Thouless (AT) line describes the boundary of replica symmetry breaking.

Purpose of the Study:

  • Investigate the ±J Ising spin glass in a magnetic field across various dimensions (d=5-8) and the Sherrington-Kirkpatrick (SK) model.
  • Determine the scaling dimension Δ associated with the ordering field.
  • Analyze the behavior of the de Almeida-Thouless (AT) line in different dimensions.

Main Methods:

  • Utilized high-temperature series expansions up to order w^10.
  • Analyzed data for d-dimensional hypercubic lattices (d=5-8) and the infinite-range SK model.
  • Examined the dependence on the magnetic field variable u=tanh^2(h/T) and temperature variable w=tanh^2(J/T).

Main Results:

  • Found scaling dimension Δ=2 in the SK model and for d≥6.
  • Observed a violation of scaling in finite fields at high dimensions, consistent with previous work.
  • Evidence supports the existence of an AT line for d≥6.
  • In d=5, exponents γ and Δ are larger than mean-field values, with no clear AT line evidence.

Conclusions:

  • Scaling is restored as dimension d approaches 6.
  • The AT line behavior is anomalous in high dimensions but shows scaling restoration near d=6.
  • Further investigation is needed for d=5, where behavior deviates significantly from mean-field predictions.