Sherrington-Kirkpatrick model: random J_ij couplings, RSB, Edwards-Anderson order parameter q_EA
SPIN CONFIGURATION (N=100)
ENERGY HISTORY
ORDER PARAMETER q(t)
Energy E/N: –
q_EA: –
Magnetization m: –
MC step: 0
T_c = J σ: –
SK Model (Sherrington-Kirkpatrick 1975): N Ising spins s_i = ±1 with random couplings J_ij ~ N(0, J²/N). Free energy has a spin-glass phase below T_c = J when replica symmetry breaks (Parisi 1979). The Edwards-Anderson order parameter q_EA = (1/N)Σ⟨s_i⟩² measures whether spins are frozen (q_EA > 0 = glass). Unlike ferromagnets, m ≈ 0 but q > 0. The energy landscape has exponentially many local minima — the system ages, never reaches equilibrium. At T < T_c ≈ 1.0 (with J=σ=1), watch q_EA rise and fluctuations grow as the system freezes.