Defect energy of infinite-component vector spin glasses.

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Disordered systems

Background:

• Vector spin glasses are complex magnetic systems with competing interactions.
• Understanding their critical behavior, especially the lower critical dimension (dl), is crucial for characterizing phase transitions.

Purpose of the Study:

• To compute the zero-temperature defect energy (ΔE) of the vector spin glass in the limit of infinite spin components (m → ∞).
• To determine how the lower critical dimension (dl) changes with an increasing number of spin components.

Main Methods:

• Numerical computation of defect energy (ΔE).
• System size scaling analysis (ΔE ∝ L^θ).
• Extrapolation to the limit of infinite spin components (m → ∞).

Main Results:

• The exponent θ was determined for dimensions 2 < d ≤ 5.
• θ values ranged from approximately -1.54 (d=2) to -0.37 (d=5).
• The lower critical dimension (dl) for m → ∞ was found to be significantly higher than for finite m (where 2 < dl < 3).

Conclusions:

• The study provides critical exponents for vector spin glasses in the m → ∞ limit.
• Results indicate a shift in the lower critical dimension, suggesting different universality classes for infinite versus finite spin components.