Critical exponents of steady-state phase transitions in fermionic lattice models

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).