= Replica symmetry breaking
<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.<Infinite Number of Order Parameters for Spin-Glasses by Giorgio Parisi>[Abstract, 3 December 1979: an infinite number of order parameters in mean-field replica theory]{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.<Nobel Lecture: Multiple equilibria by Giorgio Parisi>[§V, equations (12)–(14), overlaps between equilibrium states and their sample-dependent distribution]{ref}
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