The Ground State Energy and Concentration of Complexity in Spherical Bipartite Models

Abstract

We establish an asymptotic formula for the ground-state energy of the spherical pure $(p,q)$-spin glass model for $p,q\ge 97$. We achieve this through understanding the concentration of the complexity of critical points with values within a region of the ground state energy. More specifically, we show that the second moment of this count coincides with the square of the first moment up to a sub-exponential factor.