Self-organized criticality and the lattice topology
Response of non-equilibrium systems at criticality: ferromagnetic models in dimension two and above
We study the dynamics of ferromagnetic spin systems quenched from infinite temperature to their critical point. We perform an exact analysis of the spherical model in any dimension D>2 and numerical…
SHOWING 1-10 OF 13 REFERENCES
Abelian sandpile model.
- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
A systematic and simple method to find the correlation function of the Abelian sandpile model up to any finite order is developed. In addition, an algorithm for evaluating the distribution function…
Inverse avalanches on Abelian sandpiles.
- Geology, MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
A simple and computationally efficient way of finding inverse avalanches for Abelian sandpiles, called the inverse particle addition operator, is presented. In addition, the method is shown to be…
Self-organized critical state of sandpile automaton models.
- Computer Science, PhysicsPhysical review letters
The critical state is characterized, and its entropy for an arbitrary finite lattice in any dimension is determined, and the two-point correlation function is shown to satisfy a linear equation.
Generalized Abelian sandpile model
A sufficient condition is presented herein for which the particle addition operations commute in the eventual phase space of a general cellular automata‐type of sandpile model. The commutative nature…
Abelian sandpile model on the bethe lattice
The authors study Bak, Tang and Wiesenfeld's Abelian sandpile model (1987) of self-organised criticality on the Bethe lattice. Exact expressions for various distribution functions including the…
On the structure of absolute steady states in sandpile type of cellular automata: The geometrical aspect
It is proved that all bounded subsets of Rn with nonempty interior are cutable. Also found is an if and only if classification of when a nontrivial absolute steady state (ASS) of the sandpile‐type…
Abelian avalanches and Tutte polynomials
Equivalence between the Abelian sandpile model and the q→0 limit of the Potts model
Structure of two-dimensional sandpile. I. Height probabilities
The height probabilities of the two-dimensional Abelian sandpile model are the fractionial numbers of lattice sites having heights 1, 2, 3, 4. A combinatorial method for evaluation of these…
- PhysicsPhysical review. A, General physics