Replica Method
Spin Glasses & Parisi Replica Symmetry Breaking
Sherrington-Kirkpatrick Model
Temperature T
1.0
External field h
0.0
J variance J²
1.0
System size N
16
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Free Energy
Overlap P(q)
Configs
Observables
Free energy F/N
—
Edwards-Anderson q_EA
—
Entropy S/N
—
Phase
—
The replica trick: ln Z = lim_{n→0} (Z^n - 1)/n. Edwards-Anderson (1975) order parameter q_EA = [⟨σ⟩²]_J measures frozen disorder. Parisi (1979): replica symmetry breaking — infinitely many pure states arranged ultrametrically. The Parisi solution is exact (Guerra-Talagrand 2003). Phase diagram: paramagnetic (high T), ferromagnetic (large h), spin glass (low T, low h).