The SYK Model was originally introduced as a random matrix model for the nuclear interaction  that also describes the exponential rise of the spectral density known as  the Bethe formula. Exactly this behavior is the hallmark of the Schwarzian action, the low energy limit of the SYK model, which is the main reason for the excitement this model has brought to the field of Quantum Gravity. Another phenomenon in chaotic many-body quantum systems is the existence of  collective excitations. Remarkably, they are present in the Maldacena-Qi model of two SYK models coupled by a spin-spin interaction, which describes a phase transition between two black holes and a thermal phase. The collective state  is the ground state which is  close to a Thermo-Field Double state. We find that for systems that can be studied numerically,  the wave functions of the ground state show substantial deviations  from the Thermo-Field Double state, which suggests a non-uniform  convergence to this state in the limit of a large number of particles. The main topic of this talk is the discussion of  the thermodynamical and spectral properties of the Maldacena-Qi Model. We find a transition from Poisson  statistics in the tail of the the spectrum to RMT statistics at higher energies, when we separate the Hamiltonian  according to the spin mod 4 symmetry.  We relate this order-chaos transition to the Hawking-Page phase transition.