The Oslo rice pile model is a quenched Edwards-Wilkinson equation

Abstract

The Oslo rice pile model is a sandpile-like paradigmatic model of ``Self-Organized Criticality'' (SOC). In this paper it is shown that the Oslo model is in fact exactly a discrete realization of the much studied quenched Edwards-Wilkinson equation (qEW) [Nattermann et al., J. Phys. II France 2, 1483 (1992)]. This is possible by choosing the correct dynamical variable and identifying its equation of motion. It establishes for the first time an exact link between SOC models and the field of interface growth with quenched disorder. This connection is obviously very encouraging as it suggests that established theoretical techniques can be brought to bear with full strength on some of the hitherto elusive problems of SOC.

6 pages, 2 figures, RevTeX 4, updated version (clarified arguments and corrected references)

Cited by in corpus (20)

• 25 Years of Self-Organized Criticality: Concepts and Controversies
• Self-organization without conservation: true or just apparent scale-invariance?
• Driving-induced crossover: from classical criticality to self-organized criticality
• Feedback mechanisms for self-organization to the edge of a phase transition
• 25 Years of Self-Organized Criticality: Numerical Detection Methods
• The Oslo model, hyperuniformity, and the quenched Edwards-Wilkinson model
• Confirming and extending the hypothesis of universality in sandpiles
• Absorbing states and elastic interfaces in random media: two equivalent descriptions of self-organized criticality
• Correlations and hyperuniformity in the avalanche size of the Oslo Model
• Self-organized criticality induced by quenched disorder: experiments on flux avalanches in NbH${}_x$ films
• Anisotropy and universality: the Oslo model, the rice pile experiment and the quenched Edwards-Wilkinson equation
• The origin of power-law distributions in self-organized criticality
• Steady State and Relaxation Spectrum of the Oslo Rice-pile
• Avalanche Behavior in an Absorbing State Oslo Model
• Calculation of the transition matrix and of the occupation probabilities for the states of the Oslo sandpile model
• Dynamic roughening of the magnetic flux landscape in YBa${}_2$Cu${}_3$O${}_{7-x}$
• Reply to "Comment on `Self-organized Criticality and Absorbing States: Lessons from the Ising Model'"
• Sampling rare fluctuations of height in the Oslo ricepile model
• Patterned and Disordered Continuous Abelian Sandpile Model
• Depinning as a coagulation process