  We study the magnetic phases of a non-equilibrium spin chain, where coherent
interactions between neighboring lattice sites compete with alternating gain
and loss processes. This competition between coherent and incoherent dynamics
induces transitions between magnetically aligned and highly mixed phases,
across which the system changes from a low- to an effective
infinite-temperature state. We show that the origin of these transitions can be
traced back to the dynamical effect of parity-time-reversal symmetry breaking,
which has no counterpart in the theory of equilibrium phase transitions. This
mechanism also results in very atypical features and we find first-order
transitions without phase co-existence and mixed-order transitions which do not
break the underlying $U(1)$ symmetry, even in the appropriate thermodynamic
limit. Thus, despite its simplicity, the current model considerably extends the
phenomenology of non-equilibrium phase transitions beyond that commonly assumed
for driven-dissipative spins and related systems.
