Fixed-Energy Sandpiles Belong Generically to Directed Percolation

Basu, Mahashweta; Basu, Urna; Bondyopadhyay, Sourish; Mohanty, P. K.; Hinrichsen, Haye

doi:10.1103/physrevlett.109.015702

Cited by 66 publications

(128 citation statements)

References 37 publications

(33 reference statements)

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“…At the critical density, one expects a power-law decay of the activity with time, but this exponent is known to depend on the initial state [16]. In these models, one can characterize the structure of transient and steady state configurations in some detail.…”

Section: For Modelsmentioning

confidence: 99%

“…By adding a slow drive and dissipation, these models can be converted into models showing self-organized criticality [14]. It has recently been argued that on adding symmetry-breaking perturbations, these models would flow to DP-like critical behavior, but the evidence for this scenario is mainly numerical [15,16]. It seems worthwhile to investigate further models with conserved particle number showing active-absorbing phase transitions.…”

mentioning

confidence: 99%

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A class of exactly solved assisted-hopping models of active-inactive state transition on a line

Dandekar¹,

Dhar²

2013

EPL

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We construct a class of assisted hopping models in one dimension in which a particle can move only if it does not lie in an otherwise empty interval of length greater than n + 1. We determine the exact steady state by a mapping to a gas of defects with only on-site interaction. We show that this system undergoes a phase transition as a function of the density ρ of particles, from a low-density phase with all particles immobile for ρ ≤ ρc = 1 n+1, to an active state for ρ > ρc. The mean fraction of movable particles in the active steady state varies as (ρ − ρc) β , for ρ near ρc. We show that for the model with range n, the exponent β = n, and thus can be made arbitrarily large. Introduction -There has recently been a lot of interest in models showing an active-absorbing state transition [1][2][3]. The best studied of these is the directed percolation (DP) class [4,5], and the related pair-contact process with diffusion (PCPD) [6][7][8] and parity-conserving directed percolation (PC) [9,10]. Models with conserved number of particles where a particle may hop only if there are sufficient number of other particles present within a given range, also show an active-absorbing phase transition, where the lowdensity phase is inactive. Examples of this class are the conserved lattice gas model and the conserved threshold transfer process[11], fixed energy sandpiles [12] and the activated random walkers model [13]. By adding a slow drive and dissipation, these models can be converted into models showing self-organized criticality [14]. It has recently been argued that on adding symmetry-breaking perturbations, these models would flow to DP-like critical behavior, but the evidence for this scenario is mainly numerical [15,16]. It seems worthwhile to investigate further models with conserved particle number showing active-absorbing phase transitions.

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Section: For Modelsmentioning

confidence: 99%

mentioning

confidence: 99%

A class of exactly solved assisted-hopping models of active-inactive state transition on a line

Dandekar¹,

Dhar²

2013

EPL

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“…Much less is known about the behavior of these systems at the critical point. For comprehensive background and historical remarks we refer to [MD99,DRS10,RS12], and for ongoing discussion on the existence of an independent Manna class, see [BBB + 12,Lee13].…”

Section: Introductionmentioning

confidence: 99%

Non-equilibrium Phase Transitions: Activated Random Walks at Criticality

2014

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In this paper we present rigorous results on the critical behavior of the Activated Random Walk model. We conjecture that on a general class of graphs, including Z d , and under general initial conditions, the system at the critical point does not reach an absorbing state. We prove this for the case where the sleep rate λ is infinite. Moreover, for the one-dimensional asymmetric system, we identify the scaling limit of the flow through the origin at criticality. The case λ < +∞ remains largely open, with the exception of the one-dimensional totally-asymmetric case, for which it is known that there is no fixation at criticality.

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“…For instance, both models can be found with a bias toward a direction [34,35], or with nucleation and sinks of matter [12,26,27]. The mass can be discretized, or can be a continuous variable [33,36]. Last, we have pictured these models on one-dimensional space, but they also exist in any dimension.…”

Section: Analysis Of Symmetriesmentioning

confidence: 99%

Out-of-equilibrium stationary states, percolation, and subcritical instabilities in a fully nonconservative system

et al. 2016

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The exploration of the phase diagram of a minimal model for barchan fields leads to the description of three distinct phases for the system: stationary, percolable and unstable. In the stationary phase the system always reaches an out of equilibrium, fluctuating, stationary state, independent of its initial conditions. This state has a large and continuous range of dynamics, from dilute -where dunes do not interact -to dense, where the system exhibits both spatial structuring and collective behavior leading to the selection of a particular size for the dunes. In the percolable phase, the system presents a percolation threshold when the initial density increases. This percolation is unusual, as it happens on a continuous space for moving, interacting, finite lifetime dunes. For extreme parameters, the system exhibits a sub-critical instability, where some of the dunes in the field grow without bound. We discuss the nature of the asymptotic states and their relations to well-known models of statistical physics.

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Fixed-Energy Sandpiles Belong Generically to Directed Percolation

Cited by 66 publications

References 37 publications

A class of exactly solved assisted-hopping models of active-inactive state transition on a line

A class of exactly solved assisted-hopping models of active-inactive state transition on a line

Non-equilibrium Phase Transitions: Activated Random Walks at Criticality

Out-of-equilibrium stationary states, percolation, and subcritical instabilities in a fully nonconservative system

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