When is nonreciprocity relevant?

Nonreciprocal interactions are widely observed in nonequilibrium systems, from biological or sociological dynamics to open quantum systems. Despite the ubiquity of nonreciprocity, its impact on phase transitions is not fully understood. In this work, we derive criteria to perturbatively assess whether nonreciprocity changes the universality class of pairs of asymmetrically coupled systems undergoing a phase transition. These simple criteria are stated in terms of the unperturbed critical exponents, in the spirit of the Harris criterion for disordered systems, and agree with numerical simulations. Beyond nonreciprocity, our approach provides guidelines for assessing how dynamical phase transitions are affected by perturbations.