Liquid-Gas Criticality of Hyperuniform Fluids

TL;DR

This work shows that non-equilibrium hyperuniform fluids with center-of-mass conservation can alter liquid-gas critical behavior away from the Ising universality class. By combining a non-equilibrium field theory with a hydrodynamic Model B–like description and large-scale simulations of a 2D active-spinner system, the authors reveal a calm yet highly susceptible LG critical point characterized by finite $S(q)$ as $q\to0$ ($\eta=0$), divergent compressibility, Gaussian density fluctuations, and a scale-dependent generalized FDR with $T_{\rm eff}(q)\propto q^2$. Renormalization-group analysis shows the upper critical dimension reduces from $d_c=4$ to $d_c=2$, with mean-field–like exponents and hyperuniformity persisting for $d<d_c$. Spinodal decomposition near criticality exhibits non-conventional dynamics, including diverging waiting times without a diverging length scale. Together, these results illustrate how non-equilibrium forces can fundamentally reshape universality classes and fluctuation–dissipation relations in soft matter systems.

Abstract

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 $S(q)\sim q^η$ with $η=0$, 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 pairwise 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 $2\mathrm{Im}~ χ(q,ω) ={ω}C(q,ω)/{k_B T_{\text{eff}}(q)}$ 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.

Figures (6)

• Figure 1: (a) Schematic of dissipation-induced phase separation (DIPS) of one-component active spinner fluids, where spinner color (from blue to red) encodes the magnitude of spinners' translational kinetic energy $T_t$. (b) The phase diagram of system in dimension of density $\rho$ and driven torque $\Omega$, where the absorbing state (cyan), HU fluids (red), phase coexistence (green) regimes are depicted. (c) Structure factor $S(q)$ under different $\Omega$ at the critical density $\rho_c=0.7\sigma^{-2}$. Snapshots of absorbing state (d), HU fluids (e), LG critical point (f), phase coexistence (g). Corresponding movies (Movie S1-S4) are provided in SM supmat.
• Figure 2: Comparison of the pairwise correlation functions between 2D HU fluids (a) and 2D equilibrium Lennard-Jones fluids (b) near the LG critical point, where $\Omega_c$ ( $T_c$) is the critical torque (temperature) and $\Delta \Omega$ ($\Delta T$) is the distance from it.
• Figure 3: Hydrodynamic theory of active spinner: (a) Theoretical prediction of average collision frequency$\Bar{Z}$ as a function of $T_{t0}$ or $\rho_0$ compared with simulation results under fixed $\rho_0$ (red line) or external torque $\Omega$ (green line). (b) Translational kinetic energy as function of $\rho_0$. (c) Effective bulk chemical potential $\mu_b$ as function of $\rho_0$, where a Maxwell construction can be done for the $\Omega=15 \epsilon$. (d) Theoretical phase diagram similar to Fig. 1(b).
• Figure 4: (a) Kinetic energy spectrum $T_t( q) = \langle \vert v(q) \vert^2 \rangle/2$ of active spinner systems. (b,c) Effective temperature of spinner systems at $\Delta \Omega/\Omega_c=-0.12$ (b) and 2D stochastic field at $\Delta r/r_c=-0.16$ (c). $k_B T_{\text{eff}}(q)$ is defined by the generalized FDR Eq. (\ref{['GFDR']}) and Eq. (\ref{['GFDRstatic']}).
• Figure 5: Simulation results of 2D stochastic field. (a) structure factor for system at different distance from critical point $\tau$. (b) correlation function and response function near the critical point. Finite-size scaling analysis for (c) order parameter, (d) response to external field, (e) density fluctuations, (f) compressibility, (g) Binder cumulant and (h) energy fluctuation near the LG critical point, where $\hat{c}_v(\tau,L) = {c}_v(\tau,L) - c_0 L^{-\lambda} - c_1 \tau L^{1/\nu - \lambda}$.