Following the Ground States ofFull-RSBSpherical Spin Glasses

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 that 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 xi(x)it provides an algorithm of time complexityO(N-deg(xi))to find w.h.p. points with the ground-state energy, up to a small error. For the pure spherical models, the same algorithm reaches the energy-E-infinity, the conjectural terminal energy for gradient descent. Using the TAP formula for the free energy, for full-RSB models with support[0,q], we are able to prove the correct lower bound on the free energy (namely, prove the lower bound from Parisi's formula), assuming the correctness of the Parisi formula only in the replica symmetric case. (c) 2020 Wiley Periodicals LLC

Automated summary

The paper focuses on spherical spin glasses with support[0,q], constructing paths to find ground-state energy points on the sphere using a greedy strategy. It provides an algorithm to solve this problem efficiently. Additionally, for full-RSB models with support[0,q], the correct lower bound on the free energy is proven by the authors.