Sherrington-Kirkpatrick Spin Glass: Replica Symmetry Breaking

The SK model — random Ising spins with all-to-all random couplings — is solved by Parisi's replica symmetry breaking ansatz. Below Tₒ, the system freezes into an ultrametric landscape of exponentially many metastable states. The overlap distribution P(q) transitions from a delta function (replica symmetric) to a broad distribution — a fingerprint of spin glass order.

Spin configuration (N=64)
Overlap distribution P(q)
Temperature T: 1.20
Disorder J: 1.0
Field h: 0.00
Running Monte Carlo (Metropolis). P(q) tracks overlap between independent replicas — broad P(q) signals spin glass phase. Tc ≈ 1.0 for J=1.