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Center for Nonlinear Studies |
Among the typical models studied in statistical mechanics, such as the Ising, Heisenberg, six-vertex, eight-vertex, XXZ spin chain models, the Abelian Sandpile Model stands out as one which is not as closely explored. This talk will provide an introduction to the ASM model, self-organized criticality, sandpiles in nature and science, as well as connections to other models. In particular, the connection between the abelian sandpile model and the dimer model on grid graphs will be examined. Results concerning symmetric sandpiles will also be presented through the use of spanning tree and perfect matchings techniques, such as the Temperley and the Kenyon-Propp-Wilson bijections. The talk will end in a presentation of open problems in the ASM, as well as possible connections with other typical models in statistical mechanics.
Host: Kipton Barros, T-4 and CNLS