For high-dimensional superpositions of random plane waves, the authors derive annealed complexity formulas and a Parisi-type variational principle for the mean ground-state energy, with replica-symmetric, one-step, and full replica-symmetry-broken phases.
The Spherical p+s Spin Glass At Zero Temperature
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abstract
We determine the structure of the Parisi measure at zero temperature for the spherical p+s spin glass model. We show that depending on the values of p and s, four scenarios may emerge, including the existence of 1-FRSB and 2-FRSB phases as predicted by Crisanti and Leuzzi [10, 11]. We also provide consequences for the model at low temperature.
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Superposition of plane waves in high spatial dimensions: from landscape complexity to the deepest minimum value
For high-dimensional superpositions of random plane waves, the authors derive annealed complexity formulas and a Parisi-type variational principle for the mean ground-state energy, with replica-symmetric, one-step, and full replica-symmetry-broken phases.