  We study a diluted mean-field spin glass model with a quadratic Hamiltonian.
Our main result establishes the limiting free energy in terms of an integral of
a family of random variables that are the weak limits of the quenched variances
of the spins in the system with varying edge connectivity. The key ingredient
in our argument is played by the identification of these random variables as
the unique solution to a recursive distributional equation. Our results in
particular provide the first example of the diluted Shcherbina-Tirozzi model,
whose limiting free energy can be derived at any inverse temperature and
external field.
