Universal structures in some mean field spin glasses and an application

We discuss a spin glass reminiscent of the random energy model (REM), which allows, in particular, to recast the Parisi minimization into a more classical Gibbs variational principle, thereby shedding some light into the physical meaning of the order parameter of the Parisi theory. As an application, we study the impact of an extensive cavity field on Derrida's REM: Despite its simplicity, this model displays some interesting features such as ultrametricity and chaos in temperature.