Liquid-Gas Criticality of Hyperuniform Fluids

In statistical physics, it is well established that the liquid-gas (LG) phase transition with divergent critical fluctuations belongs to the Ising universality class. Whether non-equilibrium effects can alter this universal behavior remains a fundamental open question. In this work, we theoretically prove that non-equilibrium hyperuniform (HU) fluids with additional center-of-mass conservation exhibit LG criticality different from the Ising universality class. As a specific case, we investigate a 2D HU fluid composed of active spinners, where phase separation is driven by dissipative collisions. Strikingly, at the critical point, the 2D HU fluid displays finite density fluctuations $S(q)\sim q^{\eta}$ with $\eta=0$, while the compressibility still diverges. The critical point is thus calm yet highly susceptible, in fundamental violation of the conventional fluctuation-dissipation relation. Consistently, we observe short-range pair correlation functions coexisting with quasi-long-range response functions at the critical point. Based on a generalized Model B and renormalization-group analysis, we prove that hyperuniformity reduces the upper critical dimension $d_c$ from $4$ to $2$. Moreover, the critical point exhibits Gaussian density fluctuations and non-divergent energy fluctuations. Furthermore, the HU fluid undergoes non-conventional spinodal decomposition. The origin of the above anomalies lies in the non-equilibrium nature of the system which obeys a generalized fluctuation-dissipation relation $2\mathrm{Im}~ \chi(q,\omega) ={\omega }C(q,\omega)/{k_B T_{\text{eff}}(q)}$ with a scale-dependent effective temperature $T_{\rm eff}(q) \propto q^2$. These findings establish a striking exception to conventional paradigms of critical phenomena and illustrate how non-equilibrium forces can fundamentally reshape universality classes.