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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]

Syukuro Manabe and Klaus Hasselmann each received one quarter for physical climate models quantifying variability and predicting global warming. Giorgio Parisi received one half for discovering how disorder and fluctuations interact in physical systems from atomic to planetary scales.^[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]