SK model · Replica symmetry breaking · P(q) reveals ultrametricity
The Sherrington-Kirkpatrick (SK) model has random couplings J_ij ~ N(0,J/√N). Below T_c=J, Parisi's replica symmetry breaking (RSB) solution predicts a continuous distribution P(q) of overlaps between replicas.
Above T_c: P(q) = δ(q). Below T_c with RSB: P(q) has weight at all q ∈ [0,q_EA]. The non-trivial structure encodes ultrametricity of the energy landscape.
Parisi's 1979 solution won the Nobel Prize 2021.