Free Energy and Complexity of Spherical Bipartite Models

We investigate both free energy and complexity of the spherical bipartite spin glass model. We first prove a variational formula in high temperature for the limiting free energy based on the well-known Crisanti–Sommers representation of the mixed $$p$$p-spin spherical model. Next, we show that the mean number of local minima at low levels of energy is exponentially large in the size of the system and we derive a bound on the location of the ground state energy.

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