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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]

A spin glass has frozen, irregular local spin magnetization without the periodic magnetic order of a simple ferromagnet or antiferromagnet. Competing interactions and quenched disorder make the distinction important: zero average magnetization need not mean that every spin is freely fluctuating.^[ref]

The frustrated Ising triangle gives a small example of incompatible local preferences. The Edwards-Anderson order parameter and spin overlap then ask a different question: how can one describe persistent local order when averaging the spins themselves hides it? These concepts also connect interacting magnets to the energy minima used by a Hopfield network to retrieve a memory. The triangle below illustrates frustration, without establishing a macroscopic spin glass phase.