Sherrington-Kirkpatrick Model
H = −Σᵢⱼ Jᵢⱼ sᵢ sⱼ − h Σᵢ sᵢ
Jᵢⱼ ~ N(0, J/√N) (random!)
Each bond: ferromagnet or antiferromagnet
Frustration: can't satisfy all bonds
Statistics
Energy E—
Magnetization m—
Frustrated bonds—
Accepted moves/step—
T_c (SK) ≈ J1.00 J
Key Physics
• Many metastable states
• Exponential barriers ~ N
• Non-ergodic below T_c
• Replica symmetry breaking
(Parisi 1979, Nobel 2021)
• Overlap q_EA = order param