Combinatorial Models of Rigidity and Renormalization

Julien Barré (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We first introduce the percolation problems associated with the graph theoretical concepts of (k,l)-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for (k,l)-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of (k,l)-percolation problems on hierarchical graphs, for k≤l<2k. We introduce and solve by renormalization such a model, which has the interesting feature of showing both ordinary percolation and rigidity percolation phase transitions, depending on the values of the parameters.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Julien Barré. Combinatorial Models of Rigidity and Renormalization. Journal of Statistical Physics, 2012, 146, pp.359. ⟨hal-00764936⟩