Replica Trick & Disordered Free Energy

Parisi solution · spin glass order parameter · RSB phase structure

Parameters

Order Parameters

T_c (SK critical):1.00
Phase:-
q_EA (Edwards-Anderson):-
Free energy F:-
Replica trick:
ln Z = lim_{n→0} (Z^n−1)/n
Average over disorder: analytically continue integer n to real n→0.

Sherrington-Kirkpatrick model (1975): Random couplings J_ij ~ N(0,J²/N).

Parisi (1979): Full RSB via ultrametric overlap matrix Q_ab. Solution exact — proved by Guerra (2003) + Talagrand (2006).