  We discuss reservoir induced phase transitions of lattice fermions in the
non-equilibrium steady state (NESS) of an open system with local reservoirs.
These systems may become critical in the sense of a diverging correlation
length upon changing the reservoir coupling. We here show that the transition
to a critical state is associated with a vanishing gap in the damping spectrum.
It is shown that although in linear systems there can be a transition to a
critical state there is no reservoir-induced quantum phase transition between
distinct phases with non-vanishing damping gap. We derive the static and
dynamical critical exponents corresponding to the transition to a critical
state and show that their possible values, defining universality classes of
reservoir-induced phase transitions are determined by the coupling range of the
independent local reservoirs. If a reservoir couples to N neighboring lattice
sites, the critical exponent can assume all fractions from 1 to 1/(N - 1).
