de Almeida-Thouless instability in short-range Ising spin glasses

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.