Andrea Sportiello

Computer Science Laboratory of Paris-North University, University of Paris 13, Paris

"The identity of the Abelian Sandpile Model"

The Abelian Sandpile Model is a model for avalanches in out-of-equilibrium statistical mechanics, paradigm of self-organised criticality. In the 90's, mostly Dhar and collaborators elucidated a series of remarkable exact results in this model, which related to various branches of combinatorics. Among other things, a group structure on the recurrent configurations of the system emerged. The simplest geometry is a square portion of the 2D square lattice. In this case, the group-identity configuration shows, in the thermodynamic limit, convergence to a peculiar fractal shape, composed of infinitely-many polygons, filled with different bi-periodic patterns. The determination of this shape has been an open problem for a few decades. Here we describe the solution.