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Giorgio Parisi developed a hierarchical description of spin glass order in mean-field theory. The large number of competing low-energy states requires more information than one scalar order parameter: the replica construction uses an infinite hierarchy, related to overlaps between states. This organizes complex collective behavior arising from frustrated interactions and disorder. The result is a specific mean-field solution strategy, rather than an assumption that every disordered material has an identical phase structure.^[ref]

A physicist who researched spin glasses and became a professor of theoretical physics in Rome in 1981.^[ref]

Giorgio Parisi's 1979 work replaced a single replica order parameter by an infinite hierarchy in the mean-field theory of spin glasses. The claim concerns a thermodynamic model, rather than inequivalence of the labels attached to two finite laboratory copies.^[ref]

For equilibrium states with weights $w_{\alpha }$ and local means $m_i^{\alpha }$, define $Q_{\alpha \gamma }=N^{-1}{\sum }_i{m}_i^{\alpha }{m}_i^{\gamma }$. The distribution $P_J(q)={\sum }_{\alpha ,\gamma }{w}_{\alpha }{w}_{\gamma }\delta (q-Q_{\alpha \gamma })$ records their similarities. This state-based overlap distribution is distinct from the finite instantaneous spin overlap used in the triangle example.^[ref]