Universality class of Ising critical states with long-range losses

We show that spatial resolved dissipation can act on d-dimensional spin systems in the Ising universality class by qualitatively modifying the nature of their critical points. We consider power-law decaying spin losses with a Lindbladian spectrum closing at small momenta as propto q^α, with α a positive tunable exponent directly related to the power-law decay of the spatial profile of losses at long distances, 1/r^(α+d). This yields a class of soft modes asymptotically decoupled from dissipation at small momenta, which are responsible for the emergence of a critical scaling regime ascribable to the non-unitary counterpart of the universality class of long-range interacting Ising models. For α<1 we find a non-equilibrium critical point ruled by a dynamical field theory described by a Langevin model with coexisting inertial $sim {partial²_t}$ and frictional $sim {partial_t}$ kinetic coefficients, and driven by a gapless Markovian noise with variance propto q^α at small momenta. This effective field theory is beyond the Halperin-Hohenberg description of dynamical criticality, and its critical exponents differ from their unitary long-range counterparts. Our work lays out perspectives for a revision of universality in driven-open systems by employing dark states taylored by programmable dissipation.