Antonio Auffinger, Julian Gold
Published 2020-07-17Version 1
We show that the quenched complexity of saddles of the spherical pure $p$-spin model agrees with the annealed complexity when both are positive. Precisely, we show that the second moment of the number of critical values of a given finite index in a given interval has twice the growth rate of the first moment.
Comments: 52 pages, 1 figure
Shattering in the Ising Pure $p$-Spin Model
Griffiths inequalities for the $O(N)$-spin model
The free energy of spherical pure $p$-spin models -- computation from the TAP approach
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