Large time zero temperature dynamics of the spherical p=2-spin model of finite size

We revisit the long time dynamics of the spherical fully connected p = 2-spin glass model, when the number of spins N is large but finite. At T = 0 where the system is in a (trivial) spin-glass phase, and on long time scale t greater than or similar to O(N-2/3) we show that the behavior of physical observables, like the energy, correlation and response functions, is controlled by the density of near-extreme eigenvalues at the edge of the spectrum of the coupling matrix J, and are thus non self-averaging. We show that the late time decay of these observables, once averaged over the disorder, is controlled by new universal exponents which we compute exactly.