Following the ground-states of full-RSB spherical spin glasses

Understand

We focus on spherical spin glasses whose Parisi distribution has support of the form $[0,q]$.

• For such models we construct paths from the origin to the sphere which consistently remain close to the ground-state energy on the sphere of corresponding radius.
• The construction uses a greedy strategy, which always follows a direction corresponding to the most negative eigenvalues of the Hessian of the Hamiltonian.
• For finite mixtures $\nu(x)$ it provides an algorithm of time complexity $O(N^{{\rm deg}(\nu)})$ to find w.h.p.