Hydrodynamics, density fluctuations, and universality in conserved stochastic sandpiles

Sayani Chatterjee, Arghya Das, and Punyabrata Pradhan
Phys. Rev. E 97, 062142 – Published 22 June 2018

Abstract

We study conserved stochastic sandpiles (CSSs), which exhibit an active-absorbing phase transition upon tuning density ρ. We demonstrate that a broad class of CSSs possesses a remarkable hydrodynamic structure: There is an Einstein relation σ2(ρ)=χ(ρ)/D(ρ), which connects bulk-diffusion coefficient D(ρ), conductivity χ(ρ), and mass fluctuation, or scaled variance of subsystem mass, σ2(ρ). Consequently, density large-deviations are governed by an equilibrium-like chemical potential μ(ρ)lna(ρ), where a(ρ) is the activity in the system. By using the above hydrodynamics, we derive two scaling relations: As Δ=(ρρc)0+, ρc being the critical density, (i) the mass fluctuation σ2(ρ)Δ1δ with δ=0 and (ii) the dynamical exponent z=2+(β1)/ν, expressed in terms of two static exponents β and ν for activity a(ρ)Δβ and correlation length ξΔν, respectively. Our results imply that conserved Manna sandpile, a well studied variant of the CSS, belongs to a distinct universality—not that of directed percolation (DP), which, without any conservation law as such, does not obey scaling relation (ii).

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  • Received 18 September 2017
  • Revised 22 December 2017

DOI:https://doi.org/10.1103/PhysRevE.97.062142

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Sayani Chatterjee, Arghya Das, and Punyabrata Pradhan

  • Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block - JD, Sector - III, Salt Lake, Kolkata 700106, India

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Issue

Vol. 97, Iss. 6 — June 2018

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