  We show that the symmetry-breaking gap of the quantum Ising model in the
transverse field can be extracted from free evolution of the longitudinal
magnetization taking place after a gradual quench of the magnetic field. We
perform for this purpose numerical simulations of the Ising chains with either
periodic or open boundaries. We also study the condition for adiabaticity of
evolution of the longitudinal magnetization finding excellent agreement between
our simulations and the prediction based on the Kibble-Zurek theory of
non-equilibrium phase transitions. Our results should be relevant for ongoing
cold atom and ion experiments targeting either equilibrium or dynamical aspects
of quantum phase transitions. They could be also useful for benchmarking D-Wave
machines.
