  Short-time dynamics of many-body systems may exhibit non-analytical behavior
of the systems' properties at particular times, thus dubbed dynamical quantum
phase transition. Simulations showed that in the presence of disorder new
critical times appear in the quench evolution of the Ising model. We study the
physics behind these new critical times. We discuss the spectral features of
the Ising model responsible for the disorder-induced phase transitions. We
found the critical value of the disorder sufficient to induce the dynamical
phase transition as a function of the number of spins. Most importantly, we
argue that this dynamical phase transition while non-topological lacks a local
order parameter.
