  For the prototypical example of the Ising chain in a transverse field, we
study the impact of decoherence on the sweep through a second-order quantum
phase transition. Apart from the advance in the general understanding of the
dynamics of quantum phase transitions, these findings are relevant for
adiabatic quantum algorithms due to the similarities between them. It turns out
that (in contrast to first-order transitions studied previously) the impact of
decoherence caused by a weak coupling to a rather general environment increases
with system size (i.e., number of spins/qubits), which might limit the
scalability of the system.
