184 research outputs found
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
Power spectra of self-organized critical sandpiles
We analyze the power spectra of avalanches in two classes of self-organized
critical sandpile models, the Bak-Tang-Wiesenfeld model and the Manna model. We
show that these decay with a power law, where the exponent value
is significantly smaller than 2 and equals the scaling exponent
relating the avalanche size to its duration. We discuss the basic ingredients
behind this result, such as the scaling of the average avalanche shape.Comment: 7 pages, 3 figures, submitted to JSTA
Paths to Self-Organized Criticality
We present a pedagogical introduction to self-organized criticality (SOC),
unraveling its connections with nonequilibrium phase transitions. There are
several paths from a conventional critical point to SOC. They begin with an
absorbing-state phase transition (directed percolation is a familiar example),
and impose supervision or driving on the system; two commonly used methods are
extremal dynamics, and driving at a rate approaching zero. We illustrate this
in sandpiles, where SOC is a consequence of slow driving in a system exhibiting
an absorbing-state phase transition with a conserved density. Other paths to
SOC, in driven interfaces, the Bak-Sneppen model, and self-organized directed
percolation, are also examined. We review the status of experimental
realizations of SOC in light of these observations.Comment: 23 pages + 2 figure
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