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The mixed spherical models were recently found to violate long-heldassumptions about mean-field glassy dynamics. In particular, the thresholdenergy, where most stationary points are marginal and that in the simpler puremodels attracts long-time dynamics, seems to lose significance. Here, wecompute the typical distribution of stationary points relative to each other inmixed models with a replica symmetric complexity. We examine the stability ofnearby points, accounting for the presence of an isolated eigenvalue in theirspectrum due to their proximity. Despite finding rich structure not present inthe pure models, we find nothing that distinguishes the points that do attractthe dynamics. Instead, we find new geometric significance of the old thresholdenergy, and invalidate pictures of the arrangement of most marginal inherentstates into a continuous manifold.

Arrangement of nearby minima and saddles in the mixed spherical energy landscapes