Title: Out-of-equilibrium spherical model with correlated noise: critical phenomena, long-range correlation, and hyperuniformity

Abstract: Non-equilibrium noises, such as 1/f noise, often have long-range spatio-temporal correlations. How do such correlations affect the critical phenomena? To answer this question, we consider a spherical model driven by non-equilibrium correlated noise that does not satisfy the detailed balance. The correlation of the noise in the Fourier space is represented as $D(\boldsymbol{q},\omega) =|\boldsymbol{q}|^{-2\rho}|\omega|^{-2\theta}$, where $\boldsymbol{q}$ denotes the wave vector, and $\omega$ denotes the frequency. In most previous studies, the values of $\rho$ and $\theta$ have been limited to $0<\rho<d/2$ and $0<\theta<1/2$, where the noise correlation decreases algebraically and monotonically in real space. For $\rho<0$ or $\theta<0$, on the contrary, $D(\boldsymbol{q},\omega)$ vanishes for small $|\boldsymbol{q}|$ or $|\omega|$, namely, the fluctuation of the noise in large spatial-temporal scale is highly suppressed. Here we also consider the latter case, partially motivated by recent numerical simulations of particle systems driven by the center of mass conserving dynamics, the fluctuation of which is highly suppressed on the large spatial scale. When $\rho=\theta=0$, our model reduces to the equilibrium model, where the standard Ising universality class is observed. On the contrary, when $\rho\neq 0$ or $\theta\neq 0$, we find different universality classes, for which the critical exponents vary depending on $\rho$ and $\theta$. We also discuss that the fluctuation of the conserved order parameter exhibits the power-low correlation or hyperuniformity even well above the critical point.