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The quantum Almeida-Thouless line in the self-overlap-corrected quantum Sherrington-Kirkpatrick model
Chokri Manai, Simone Warzel · 2026-05-19 · via math.PR updates on arXiv.org

We present a complete analysis of the glass transition in the self-overlap-corrected Sherrington-Kirkpatrick (SK) model in a transverse magnetic field, also referred to as the quantum SK model. In particular, we determine the phase boundary separating the glassy and paramagnetic phases. The proof is based on a simplified Parisi variational principle for the quantum pressure, which only involves classical Parisi order parameters. As part of the proof, we also analyze the pressure of the self-overlap-constrained quantum SK model and its Parisi description, as well as the pressure of generalized quantum Hopfield models.

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