  We study the current-carrying steady-state of a transverse field Ising chain
coupled to magnetic thermal reservoirs and obtain the non-equilibrium phase
diagram as a function of the magnetization potential of the reservoirs. Upon
increasing the magnetization bias we observe a discontinuous jump of the
magnetic order parameter that coincides with a divergence of the correlation
length. For steady-states with a non-vanishing conductance, the entanglement
entropy at zero temperature displays a bias dependent logarithmic correction
that violates the area law and differs from the well-known equilibrium case.
Our findings show that out-of-equilibrium conditions allow for novel critical
phenomena not possible at equilibrium.
