The variance of any perturbation operator satisfying two mild assumptions vanishes in the thermodynamic limit, ruling out non-spontaneous replica symmetry-breaking.
The Ghirlanda-Guerra identities without averaging
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abstract
The Ghirlanda-Guerra identities are one of the most mysterious features of spin glasses. We prove the GG identities in a large class of models that includes the Edwards-Anderson model, the random field Ising model, and the Sherrington-Kirkpatrick model in the presence of a random external field. Previously, the GG identities were rigorously proved only `on average' over a range of temperatures or under small perturbations.
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Self-averaging of perturbation Hamiltonian density in perturbed spin systems
The variance of any perturbation operator satisfying two mild assumptions vanishes in the thermodynamic limit, ruling out non-spontaneous replica symmetry-breaking.