Rotational sandpile models: A finite size scaling study
Abstract Nontrivial critical behaviour is observed in equilibrium lattice statistical models under rotational constraint. Effect of rotational constraint on lattice statistical models at out of equilibrium situation is important to study. Critical properties of non-equilibrium steady state of sandpile models are studied under rotational constraint via finite size scaling (FSS) analysis. Not only FSS is found to be valid for a wide range of rotational sandpile models but also they are found to belong to the same universality class.
Characteristics of deterministic and stochastic sandpile models in a rotational sandpile model.
Rotational constraint representing a local external bias generally has a nontrivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in an out-of-equilibrium situation like self-organized criticality, a two state "quasideterministic" rotational sandpile model is developed here imposing rotational constraint on the flow of sand grains. An extended set of critical exponents are estimated to characterize the avalanche properties at the nonequilibrium 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.
Structure of avalanches and breakdown of simple scaling in the Abelian sandpile model in one dimension.
We study the Abelian sandpile model on decorated one dimensional chains. We show that there are two types of avalanches, and determine the effects of finite, though large, system size L on the asymptotic form of distributions of avalanche sizes, and show that these differ qualitatively from the behavior on a simple linear chain. For large L, we find that the probability distribution of the total number of topplings s is not described by a simple finite-size scaling form, but by a linear combination of two simple scaling forms: ${\mathrm{Prob}}_{\mathit{L}}$(s)=(1/L)${\mathit{f}}_{1}$(s/L)+(1/${\mathit{L}}^{2}$)${\mathit{f}}_{2}$(s/${\mathit{L}}^{2}$), where ${\mathit{f}}_{1}$ and ${\mathit{f}}_{2}$ are nonuniversal scaling functions of one argument.