Sherrington-Kirkpatrick model · Edwards-Anderson order parameter · RS solution
Parameters
Replica Equations
ln Z ≈ n⁻¹ [⟨Zⁿ⟩_J − 1] as n→0
f = −T lim_{n→0} (∂/∂n)⟨Zⁿ⟩_J
q_EA = [⟨σᵢ⟩²]_J (RS ansatz)
q = ∫Dz tanh²(z√(β²J²q)+βh)
Solving RS self-consistency...
Physics
The replica trick uses the identity ln Z = lim_{n→0}(Zⁿ−1)/n to average over disorder. The RS ansatz assumes all replicas are equivalent, yielding the self-consistency equation for q. Below Tc=J, the spin glass phase has q>0 — spins freeze in random orientations. RS is unstable below Tc (Parisi RSB needed).