scholarly journals Any Shape Can Ultimately Cross Information on Two-Dimensional Abelian Sandpile Models

2018 ◽  
pp. 127-142
Author(s):  
Viet-Ha Nguyen ◽  
Kévin Perrot
Keyword(s):  
Two Dimensional ◽  
Abelian Sandpile ◽  
Sandpile Models

scholarly journals Sandpile Models in the Large

2021 ◽  
Vol 9 ◽  
Author(s):  
Philippe Ruelle
Keyword(s):  
Field Theory ◽  
Boundary Conditions ◽  
Spanning Tree ◽  
Large Scale ◽  
Two Dimensional ◽  
Critical Systems ◽  
Abelian Sandpile ◽  
Scale Properties ◽  
Sandpile Models ◽  
Theoretic Description

This contribution is a review of the deep and powerful connection between the large-scale properties of critical systems and their description in terms of a field theory. Although largely applicable to many other models, the details of this connection are illustrated in the class of two-dimensional Abelian sandpile models. Bulk and boundary height variables, spanning tree–related observables, boundary conditions, and dissipation are all discussed in this context and found to have a proper match in the field theoretic description.

scholarly journals CLASSICAL TWO-DIMENSIONAL SANDPILE MODELS

2016 ◽  
Vol 24 (4) ◽  
pp. 39-70 ◽  
Author(s):  
A. V. Podlazov ◽  
Keyword(s):  
Two Dimensional ◽  
Sandpile Models

scholarly journals Extra investigation of the self-organized critical Manna model at higher critical dimension

2021 ◽  
pp. 1-12
Author(s):  
Andrey Viktorovich Podlazov
Keyword(s):  
Power Law ◽  
Critical Dimension ◽  
The Self ◽  
Two Dimensional ◽  
Upper Critical Dimension ◽  
Self Organized ◽  
Logarithmic Corrections ◽  
Universal Indicator ◽  
Sandpile Models ◽  
Power Law Distributions

I investigate the nature of the upper critical dimension for isotropic conservative sandpile models and calculate the emerging logarithmic corrections to power-law distributions. I check the results experimentally using the case of Manna model with the theoretical solution known for all statement starting from the two-dimensional one. In addition, based on this solution, I construct a non-trivial super-universal indicator for this model. It characterizes the distribution of avalanches by time the border of their region needs to pass its width.

Critical exponents for boundary avalanches in two-dimensional Abelian sandpile

1994 ◽  
Vol 27 (16) ◽  
pp. L585-L590 ◽  
Author(s):  
E V Ivashkevich ◽  
D V Ktitarev ◽  
V B Priezzhev
Keyword(s):  
Critical Exponents ◽  
Two Dimensional ◽  
Abelian Sandpile

Universality Class in Abelian Sandpile Models with Stochastic Toppling Rules

2005 ◽  
Vol 44 (3) ◽  
pp. 483-486 ◽  
Author(s):  
Gui-Jun Pan ◽  
Duan-Ming Zhang ◽  
Hong-Zhang Sun ◽  
Yan-Ping Yin
Keyword(s):  
Universality Class ◽  
Abelian Sandpile ◽  
Sandpile Models

scholarly journals Universality classes in isotropic, Abelian, and non-Abelian sandpile models

1998 ◽  
Vol 58 (1) ◽  
pp. 303-310 ◽  
Author(s):  
Erel Milshtein ◽  
Ofer Biham ◽  
Sorin Solomon
Keyword(s):  
Abelian Sandpile ◽  
Universality Classes ◽  
Sandpile Models

scholarly journals Algebraic aspects of Abelian sandpile models

1995 ◽  
Vol 28 (4) ◽  
pp. 805-831 ◽  
Author(s):  
D Dhar ◽  
P Ruelle ◽  
S Sen ◽  
D -N Verma
Keyword(s):  
Abelian Sandpile ◽  
Sandpile Models

scholarly journals CONTINUOUS ABELIAN SANDPILE MODEL IN TWO DIMENSIONAL LATTICE

2011 ◽  
Vol 25 (32) ◽  
pp. 4709-4720 ◽  
Author(s):  
N. AZIMI-TAFRESHI ◽  
E. LOTFI ◽  
S. MOGHIMI-ARAGHI
Keyword(s):  
Boundary Conditions ◽  
Small Mass ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
New Model ◽  
Different Boundary Conditions ◽  
Sandpile Model ◽  
Abelian Sandpile Model ◽  
General Properties ◽  
Abelian Sandpile

We investigate a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so the general properties of the two models are identical. Yet the new model allows us to investigate some problems such as the effect of very small mass on the height probabilities, different boundary conditions, etc.

Sign in / Sign up

Export Citation Format

Share Document