Elasticity of disordered elastic networks: Jamming, rigidity percolation and beyond

Elastic networks provide a simple and reliable framework to study rigidity transitions in a variety of disordered systems, from amorphous solids and confluent cell tissues to traditional rigidity percolation and jamming [1]. Here I will present results of a new theory [2] of the jamming transition that is both analytically tractable and that clarifies the relation between jamming and rigidity percolation. Our theory yields a faithful description of jamming, including spatial and temporal dependences in the elastic and fluid phases and crossover behavior. I will then derive scaling forms for singular dynamical responses and extract diverging length scales, critical exponents, invariant scaling combinations and explicit formulas for universal scaling functions. Finally, I will make contact with microscopy experiments of colloidal suspensions of silica particles in glycerin/water, and published measurements featuring the unusual charge response of strange metals [3].

[1] A. Liu and S. Nagel, Annu. Rev. Condens. Matter Phys. 1, 347 (2010)
[2] D. B. Liarte et al., Phys. Rev. Lett. 122, 128006 (2019)
[3] M. Mitrano et al., Proc. Natl. Acad. Sci. U.S.A. 115, 5392 (2018)