  We present two approaches to the dynamics of a quench-induced phase
transition in quantum Ising model. The first one retraces steps of the standard
approach to thermodynamic second order phase transitions in the quantum
setting. The second one is purely quantum, based on the Landau-Zener formula
for transition probabilities in avoided level crossings. We show that the two
approaches yield compatible results for the scaling of the defect density with
the quench rate. We exhibit similarities between them, and comment on the
insights they give into dynamics of quantum phase transitions.
