  We prove disorder universality of chaos phenomena and ultrametricity in the
mixed p-spin model under mild moment assumptions on the environment. This
establishes the long-standing belief among physicists that the Parisi solution
in mean-field models is universal. Our results extend to universal properties
of other physical observables in the mixed p-spin model as well as in different
spin glass models. These include universality of quenched disorder chaos in the
Edwards-Anderson (EA) model and quenched concentration for the magnetization in
both EA and mixed p-spin models under non-Gaussian environments. In addition,
we show quenched self-averaging for the overlap in the random field Ising model
under small perturbation of the external field.
