Phase transition and critical behavior in a model of organized criticality |
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Authors: | Biskup M Blanchard Ph Chayes L Gandolfo D Krüger T |
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Institution: | (1) Department of Mathematics, UCLA, Los Angeles, California, USA;(2) Department of Theoretical Physics, University of Bielefeld, Bielefeld, Germany;(3) Phymath, Department of Mathematics, University of Toulon, Toulon, France and CPT/CNRS, Luminy, Marseille, France |
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Abstract: | We study a model of ![lsquo](/content/5cfr7q0nyp3p4kby/xxlarge8216.gif) organized![rsquo](/content/5cfr7q0nyp3p4kby/xxlarge8217.gif) criticality, where a single avalanche propagates through an a priori static (i.e., organized) sandpile configuration. The latter is chosen according to an i.i.d. distribution from a Borel probability measure on 0,1]. The avalanche dynamics is driven by a standard toppling rule, however, we simplify the geometry by placing the problem on a directed, rooted tree. As our main result, we characterize which are critical in the sense that they do not admit an infinite avalanche but exhibit a power-law decay of avalanche sizes. Our analysis reveals close connections to directed site-percolation, both in the characterization of criticality and in the values of the critical exponents.Mathematics Subject Classification (2000): 60K35, 82C20, 82C44 |
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