Characteristics of Deterministic and Stochastic Sandpile Models in a Rotational Sandpile Model

Abstract

Rotational constraint representing a local external bias generally has non-trivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in a out of equilibrium situation like self-organized criticality, a new two state ``quasi-deterministic'' rotational sandpile model is developed here imposing rotational constraint on the flow of sand grains. An extended set of new critical exponents are found to characterize the avalanche properties at the non-equilibrium steady state of the model. The probability distribution functions are found to obey usual finite size scaling supported by negative time autocorrelation between the toppling waves. The model exhibits characteristics of both deterministic and stochastic sandpile models.

27 pages, 11 figures

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• Crossover from rotational to stochastic sandpile universality in the random rotational sandpile model
• Critical properties of deterministic and stochastic sandpile models on two-dimensional percolation backbone