Edwards-Anderson order parameter ($q_{\mathrm{EA}}=N^{-1}{\sum }_i⟨s_i{⟩}_{\alpha }^2$)

The Edwards-Anderson order parameter measures squared local spin magnetization within a selected equilibrium state $\alpha$. Squaring prevents opposite local orientations from cancelling. The state selection and limits matter: the full finite, zero-field canonical ensemble has $⟨s_i⟩=0$ by spin inversion symmetry, so substituting that average would miss broken-state order.^[ref]