Hydrodynamics, density fluctuations, and universality in conserved stochastic sandpiles

Area of Science:

• Statistical Physics
• Complex Systems
• Phase Transitions

Background:

• Conserved stochastic sandpiles (CSSs) are models exhibiting active-absorbing phase transitions.
• Understanding the critical behavior and universality classes of such systems is crucial.

Purpose of the Study:

• To investigate the hydrodynamic structure of CSSs.
• To derive scaling relations near the critical density.
• To determine the universality class of CSSs and compare it to directed percolation.

Main Methods:

• Analysis of the Einstein relation: σ²(ρ)=χ(ρ)/D(ρ).
• Investigation of density large-deviations governed by a chemical potential.
• Derivation of scaling relations for mass fluctuation and the dynamical exponent z.

Main Results:

• A universal Einstein relation was found for CSSs, linking diffusion coefficient D(ρ), conductivity χ(ρ), and mass fluctuation σ²(ρ).
• Density large-deviations are governed by an equilibrium-like chemical potential.
• Two scaling relations were derived, including a dynamical exponent z=2+(β-1)/ν⊥, dependent on static exponents β and ν⊥.

Conclusions:

• CSSs possess a distinct hydrodynamic structure and universality class, different from directed percolation (DP).
• The derived scaling relations are specific to systems with conservation laws, unlike DP.
• The conserved Manna sandpile is confirmed to belong to this distinct universality class.