Abelian Sandpile Model on the Husimi Lattice of Square Plaquettes

Abstract

An Abelian sandpile model is considered on the Husimi lattice of square plaquettes. Exact expressions for the distribution of height probabilities in the Self-Organized Critical state are derived. The two-point correlation function for the sites deep inside the Husimi lattice is calculated exactly.

arXiv comment12 pages, LaTeX, source files and some additional information available at http://thsun1.jinr.dubna.su/~shcher/

References in corpus (2)

• Exact solutions for a mean-field Abelian sandpile
• Tricritical Phenomena in a Z(3) Lattice Gauge Theory

Cited by in corpus (4)

• Analytical approach to directed sandpile models on the Apollonian network
• An exact solution on the ferromagnetic Face-Cubic spin model on a Bethe lattice
• Cut-off for sandpiles on tiling graphs
• The spectrum of the abelian sandpile model