For the mean-field spherical model in random fields, the paper classifies metastates and overlap distributions: continuous symmetry breaking for d>=2, with non-self-averaging, replica-symmetry-breaking overlaps when fields are scaled by 1/sqrt(n).
Uniqueness of ground states for short-range spin glasses in the half-plane
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$d$-dimensional spherical ferromagnets in random fields: Metastates, continuous symmetry breaking, and spin-glass features
For the mean-field spherical model in random fields, the paper classifies metastates and overlap distributions: continuous symmetry breaking for d>=2, with non-self-averaging, replica-symmetry-breaking overlaps when fields are scaled by 1/sqrt(n).