Non-equilibrium coupling to a diffusing density breaks Ising universality

Abstract

The Ising universality class is remarkably robust to non-equilibrium perturbations, which generically flow to zero under renormalization. We show that this robustness fails when an order parameter is coupled nonreciprocally to a conserved diffusive density. Below $d_c=4$, the renormalization group flows to a fast-diffusion fixed point at which the density acts as a long-range multiplicative noise, producing a novel universality class. The non-equilibrium nature of the fixed point is manifest in the large-scale violation of the fluctuation-dissipation relations, reflected in a splitting of the scaling exponents of the two-point correlation and response functions--a measurable hallmark of non-equilibrium critical fluctuations. A two-loop calculation establishes the stability of this fixed point but yields a small correction-to-scaling exponent $\omega\approx0.020$ in $d=3$, implying strong finite-size corrections. An all-orders modified Harris criterion $\nu>2/(d+z-2)$ confirms that the BIM fixed point governs criticality in $d=3$, with Ising universality recovered only at $d=2$.