IRMACS: The Interdisciplinary Colloquium: "Percolation and Rigidity in Disordered Networks"

Abstract

As the number of bonds connecting the sites on a regular lattice is reduced, one eventually reaches the "percolatio point" at which the last path connecting one side of the lattice to the other disappears. This is a "geometric phase transition" that has been extensively studied and that is well understood. Less well understood is the behavior of the elasticity of such networks. If the bonds represent simple springs then the elastic constants generically vanish well before the percolation point is reached, at least at zero temperature. I will argue that at nonzero temperature entropic effects restore elasticity and that the critical behavior of the elastic constants is both universal and very simple.