  We analyze signatures of the dynamical quantum phase transitions in physical
observables. In particular, we show that both the expectation value and various
out of time order correlation functions of the finite length product or string
operators develop cusp singularities following quench protocols, which become
sharper and sharper as the string length increases. We illustrated our ideas
analyzing both integrable and nonintegrable one-dimensional Ising models
showing that these transitions are robust both to the details of the model and
to the choice of the initial state.
