Phys. Rev. Lett. 104, 145703 (2010) [4 pages]Driving Sandpiles to Criticality and BeyondReceived 16 December 2009; revised 4 March 2010; published 9 April 2010 A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation. This theory predicts that the stationary density of the Abelian sandpile model equals the threshold density of the fixed-energy sandpile. We refute this prediction for a wide variety of underlying graphs, including the square grid. Driven dissipative sandpiles continue to evolve even after reaching criticality. This result casts doubt on the validity of using fixed-energy sandpiles to explore the critical behavior of the Abelian sandpile model at stationarity. © 2010 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.104.145703
DOI:
10.1103/PhysRevLett.104.145703
PACS:
64.60.av, 45.70.Cc
See AlsoComment: Hang-Hyun Jo and Hyeong-Chai Jeong, Comment on “Driving Sandpiles to Criticality and Beyond”, Phys. Rev. Lett. 105, 019601 (2010). |
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