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Patterned and disordered continuous Abelian sandpile model.

N Azimi-Tafreshi¹, S Moghimi-Araghi

¹Department of Physics, Sharif University of Technology, Tehran, Iran. azimi@physics.sharif.ir

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2009

Summary

This summary is machine-generated.

This study investigates anisotropic continuous Abelian sandpile models and directed sandpile models with randomness. We reveal how specific rules create ordered patterns and lead to a random fixed point in these complex systems.

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Area of Science:

Statistical Physics
Complex Systems
Dynamical Systems

Background:

The Abelian sandpile model is a paradigm for self-organized criticality.
Anisotropies and quenched randomness introduce complexity to sandpile models.
Understanding critical phenomena in these systems is crucial for various fields.

Purpose of the Study:

To analyze critical properties of continuous Abelian sandpile models with anisotropic toppling rules.
To investigate the critical behavior of a continuous directed sandpile model under weak quenched randomness.
To identify emergent patterns and fixed points in these perturbed sandpile systems.

Main Methods:

Analysis of continuous Abelian sandpile models with anisotropic rules.
Application of perturbative conformal field theory to the directed sandpile model.
Study of critical phenomena and pattern formation.

Main Results:

Anisotropic rules in Abelian sandpiles lead to the formation of ordered patterns.
The continuous directed sandpile model with weak quenched randomness exhibits critical behavior.
A random fixed point is identified in the perturbed directed sandpile model.

Conclusions:

Anisotropies can drive order in otherwise complex sandpile dynamics.
Perturbative conformal field theory is effective for studying critical behavior in disordered systems.
The presence of a random fixed point signifies a distinct critical state in the directed sandpile model.