Quenched complexity of marginal states in the Sherrington--Kirkpatrick spin glass

Abstract

The number of metastable states of a random corrugated landscape controls what dynamics, inference and learning can reach. In the Sherrington-Kirkpatrick model these states are marginal, and counting them requires breaking the BRST symmetry. So far only the annealed complexity was known, predicting states below equilibrium. We compute the quenched complexity function with a two-group Ansatz and one-step replica symmetry breaking. It branches continuously off the annealed curve at its instability point and vanishes near the Parisi free energy, while the soft mode turns toward orthogonality to the magnetization.

26 pages, 9 figures