  The full replica symmetry breaking free energy of the Ising spin glass on
random regular graphs is given by the solutions of two auxiliary variational
problems inside a global (physical) variational problem on the order parameter.
In this paper, we provide a detailed study of the auxiliary variational
problems. We get the self-consistency equation for the auxiliary order
parameter and obtain the existence and uniqueness results. We also show that
the full replica symmetry breaking free energy functional recovers the discrete
replica symmetry breaking solutions, by imposing some proper conditions on the
physical order parameter.
