We study the spin-1 Ising model with non-local constraints imposed by the Bak–Tang–Wiesenfeld sandpile model of self-organized criticality (SOC). The model is constructed as if the sandpile is being built on a (honeycomb) lattice with Ising interactions. In this way we combine two models...

Universality and scaling for systems driven to criticality by a tuning parameter has been well studied. However, there are very few corresponding studies for the models of self-organized criticality, e.g., the Bak, Tang, and Wiesenfeld (BTW) sandpile model. It is well known that every avalanche...

The nature of self-organized criticality (SOC) is pin-pointed with a simple mechanical model: a pinball machine. Its phase space is fully parameterized by two integer variables, one describing the state of an on-going game, the other describing the state of the machine. This is the simplest...

We study the distributions of dissipative and nondissipative avalanches separately in the stochastic Zhang (SP-Z) sandpile in two dimension. We find that dissipative and nondissipative avalanches obey simple power laws and do not have the logarithmic correction, while the avalanche distributions...

We present some analytical results for the stochastic sandpile model studied earlier by Manna. In this model, the operators corresponding to particle addition at different sites commute. The eigenvalues of operators satisfy a system of coupled polynomial equations. For an L×L square, we...

This article is based on a talk given by one of us (EVI) at the conference “StatPhys-Taipei-1997”. It overviews the exact results in the theory of the sandpile model and discusses briefly the yet unsolved problem of calculation of avalanche distribution exponents. The key ingredients include...