  We consider a spherical spin system with pure 2-spin spherical
Sherrington-Kirkpatrick Hamiltonian with ferromagnetic Curie-Weiss interaction.
The system shows a two-dimensional phase transition with respect to the
temperature and the coupling constant. We compute the limiting distributions of
the free energy for all parameters away from the critical values. The zero
temperature case corresponds to the well-known phase transition of the largest
eigenvalue of a rank 1 spiked random symmetric matrix. As an intermediate step,
we establish a central limit theorem for the linear statistics of rank 1 spiked
random symmetric matrices.
