Spin Glass — Parisi Replica Symmetry Breaking

The SK (Sherrington-Kirkpatrick) spin glass has random Gaussian couplings J_ij. Parisi's RSB solution (Nobel Prize 2021) reveals an ultrametric landscape of pure states organized in a hierarchical tree — the overlap distribution P(q) is non-trivial below T_g. Simulated here with parallel tempering Monte Carlo.

E = — | m = — | q = — | T_g ≈ 1.0