The abelian sandpile and related models
Deepak Dhar
Abstract
The Abelian sandpile model is the simplest analytically tractable model of self-organized criticality. This paper presents a brief review of known results about the model. The abelian group structure allows an exact calculation of many of its properties. In particular, one can calculate all the critical exponents for the directed model in all dimensions. For the undirected case, the model is related to q= 0 Potts model. This enables exact calculation of some exponents in two dimensions, and there are some conjectures about others. We also discuss a generalization of the model to a network of communicating reactive processors. This includes sandpile models with stochastic toppling rules as a special case. We also consider a non-abelian stochastic variant, which lies in a different universality class, related to directed percolation.
Create a lesson
Related papers
Droplets obstruct Onsager-type solutions of the Ising model in a magnetic field
Ran Luo, Jiahua Tian
Physical limits to stochastic classifiers
Timur Aslyamov, Massimiliano Esposito
Absolute area under a scaled Brownian motion with resetting
Vicenç Méndez, Javier Cristín
Understanding the Mpemba Effect through a Rule of Thumb
Ran Yaacoby
Beyond the lemon: Spectra of random Lindblad operators with a Hamiltonian component
Mykhailo Hontarenko, Wojciech Tarnowski, Sergey Denisov et al.
Towards synergy between theory and experiments: First-passage processes under resetting with stochastic return protocols
Ashutosh Dubey, Arnab Pal