Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism
Abstract
At asymptotically late times ultrametricity can emerge from the persistent slow aging dynamics of the glass phase. We show that this suffices to recover the breaking of replica symmetry in mean-field spin glasses from the late time limit of the time evolution using the Keldysh path integral. This provides an alternative approach to replica symmetry breaking by connecting it rigorously to the dynamic formulation. Stationary spin glasses are thereby understood to spontaneously break thermal symmetry, or the Kubo-Martin-Schwinger relation of a state in global thermal equilibrium. We demonstrate our general statements for the spherical quantum $p$-spin model and the quantum Sherrington-Kirkpatrick model in the presence of transverse and longitudinal fields. In doing so, we also derive their dynamical Ginzburg-Landau effective Keldysh actions starting from microscopic quantum models.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.05842
- arXiv:
- arXiv:2406.05842
- Bibcode:
- 2024arXiv240605842L
- Keywords:
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- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Strongly Correlated Electrons;
- Mathematical Physics;
- Quantum Physics
- E-Print:
- 17 pages, 4 figures, submitted version