When is nonreciprocity relevant?

Giulia Garcia Lorenzana; David Martin; Yael Avni; Daniel S. Seara; Michel Fruchart; Giulio Biroli; Vincenzo Vitelli

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arXiv · 2509.17972

When is nonreciprocity relevant?

Giulia Garcia Lorenzana·David Martin·Yael Avni·Daniel S. Seara·Michel Fruchart·Giulio Biroli·Vincenzo Vitelli

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Abstract

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 two-species systems undergoing a phase transition. These criteria, stated in terms of the unperturbed critical exponents in the spirit of the Harris criterion for disordered systems, assess whether static critical exponents change at first order under a given perturbation. For example, in the case of a nonreciprocal version of model A with two species, a homogeneous nonreciprocal perturbation is relevant whenever the two parts are initially identical and uncoupled, and irrelevant otherwise. Our results agree with existing renormalization group calculations and with numerical simulations.

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Giulia Garcia Lorenzana, David Martin, Yael Avni, Daniel S. Seara, Michel Fruchart, Giulio Biroli, Vincenzo Vitelli. 2025-09-22. When is nonreciprocity relevant?. https://arxiv.org/abs/2509.17972

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