29 research outputs found
Mapping Self-Organized Criticality onto Criticality
We present a general conceptual framework for self-organized criticality
(SOC), based on the recognition that it is nothing but the expression,
''unfolded'' in a suitable parameter space, of an underlying {\em unstable}
dynamical critical point. More precisely, SOC is shown to result from the
tuning of the {\em order parameter} to a vanishingly small, but {\em positive}
value, thus ensuring that the corresponding control parameter lies exactly at
its critical value for the underlying transition. This clarifies the role and
nature of the {\em very slow driving rate} common to all systems exhibiting
SOC. This mechanism is shown to apply to models of sandpiles, earthquakes,
depinning, fractal growth and forest-fires, which have been proposed as
examples of SOC.Comment: 17 pages tota
Finite-scale singularity in the renormalization group flow of a reaction-diffusion system
International audienceWe study the nonequilibrium critical behavior of the pair contact process with diffusion (PCPD) by means of nonperturbative functional renormalization group techniques. We show that usual perturbation theory fails because the effective potential develops a nonanalyticity at a finite length scale: Perturbatively forbidden terms are dynamically generated and the flow can be continued once they are taken into account. Our results suggest that the critical behavior of PCPD can be either in the directed percolation or in a new (conjugated) universality class
Absorbing states and elastic interfaces in random media: two equivalent descriptions of self-organized criticality
We elucidate a long-standing puzzle about the non-equilibrium universality
classes describing self-organized criticality in sandpile models. We show that
depinning transitions of linear interfaces in random media and absorbing phase
transitions (with a conserved non-diffusive field) are two equivalent languages
to describe sandpile criticality. This is so despite the fact that local
roughening properties can be radically different in the two pictures, as
explained here. Experimental implications of our work as well as promising
paths for future theoretical investigations are also discussed.Comment: 4 pages. 2 Figure
Integration of Langevin Equations with Multiplicative Noise and Viability of Field Theories for Absorbing Phase Transitions
Efficient and accurate integration of stochastic (partial) differential
equations with multiplicative noise can be obtained through a split-step
scheme, which separates the integration of the deterministic part from that of
the stochastic part, the latter being performed by sampling exactly the
solution of the associated Fokker-Planck equation. We demonstrate the
computational power of this method by applying it to most absorbing phase
transitions for which Langevin equations have been proposed. This provides
precise estimates of the associated scaling exponents, clarifying the
classification of these nonequilibrium problems, and confirms or refutes some
existing theories.Comment: 4 pages. 4 figures. RevTex. Slightly changed versio
Sticky grains do not change the universality class of isotropic sandpiles
We revisit the sandpile model with ``sticky'' grains introduced by Mohanty
and Dhar [Phys. Rev. Lett. {\bf 89}, 104303 (2002)] whose scaling properties
were claimed to be in the universality class of directed percolation for both
isotropic and directed models. Simulations in the so-called fixed-energy
ensemble show that this conclusion is not valid for isotropic sandpiles and
that this model shares the same critical properties of other stochastic
sandpiles, such as the Manna model. %as expected from the existence of an extra
%conservation-law, absent in directed percolation. These results are
strengthened by the analysis of the Langevin equations proposed by the same
authors to account for this problem which we show to converge, upon
coarse-graining, to the well-established set of Langevin equations for the
Manna class. Therefore, the presence of a conservation law keeps isotropic
sandpiles, with or without stickiness, away from the directed percolation
class.Comment: 4 pages. 3 Figures. Subm. to PR