We show that, on a $d$-dimensional hypercubic lattice with $d>1$, conserved-mass transport processes, with multidirectional hopping that respect all symmetries of the lattice, exhibit power-law correlations for generic parameter values—even far from phase transition point, if any. The key idea for generating the algebraic decay is the notion of multidirectional hopping, which means that several chunks of masses, or several particles, can hop out simultaneously from a lattice site in multiple directions, consequently breaking detailed balance. Notably, the systems we consider are described by a continuous-time Markov process, are diffusive, lattice-rotation symmetric, spatially homogeneous and thus have $\mathit{no}$ net mass current. Using hydrodynamic and exact microscopic theory, we show that, for spatial dimensions $d>1$, the steady-state static density-density and “activity”-density correlation functions in the thermodynamic limit typically decay as $\sim 1/r^{(d+2)}$ at large distance $r=\left|\mathbf{r}\right|$; the strength of the power law is exactly calculated for several models and expressed in terms of the density-dependent bulk-diffusion coefficient and Onsager matrix (or, mobility tensor). In particular, our theory explains why center-of-mass-conserving dynamics, used to model novel disordered hyperuniform state of matter, result in generic long-ranged correlations. However, in a restricted parameter regime, the correlations can also be short ranged and are characterized through the Onsager matrix.

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• Fluctuations & noise
• Irreversible processes
• Nonequilibrium lattice models
• Linear response theory
• Markovian processes
• Monte Carlo methods