Spin-s spin-glass phases in the d=3 Ising model

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Phase Transitions

Background:

• Spin glasses are complex magnetic systems exhibiting quenched disorder.
• Understanding the influence of spin magnitude (s) on phase transitions is crucial.
• Renormalization-group (RG) theory provides a powerful framework for studying critical phenomena.

Purpose of the Study:

• To investigate the behavior of higher-spin (s≥1/2) Ising spin glasses in three spatial dimensions (d=3).
• To determine the impact of increasing spin values on global phase diagrams and critical exponents.
• To analyze the chaotic dynamics and phase transition nature in these systems.

Main Methods:

• Renormalization-group (RG) theory applied to a 3D hierarchical model.
• Migdal-Kadanoff approximation utilized on a cubic lattice.
• Calculation of phase diagrams, Lyapunov exponent, and spin-glass runaway exponent.

Main Results:

• A finite-temperature spin-glass phase exists for all spin values (s) in d=3, including the continuum limit (s→∞).
• Phase diagrams saturate to a limit value as spin (s) increases.
• The spin-glass phase exhibits chaotic behavior (Lyapunov exponent λ=1.93) and strong-coupling dynamics.
• Ferromagnetic-spin-glass and spin-glass-antiferromagnetic transitions occur at fixed concentrations (p_t=0.37 and 0.63) and are independent of spin (s).

Conclusions:

• The existence of a robust spin-glass phase across all spin values in 3D is confirmed.
• The observed phase transitions are predominantly percolative and insensitive to spin magnitude.
• Higher-spin Ising spin glasses display simultaneous strong-chaos and strong-coupling characteristics.