Structural disorder can strongly alter the behavior of a material, however, and presents a serious challenge to the theorist since translational symmetry can no longer be exploited.
Percolation theory is the simplest, most generic model of a disordered material.
We are studying the fractal geometry of the clusters in percolation using large-scale numerical simulations. We have also developed exact mappings of percolation onto other problems in statistical physics. These mappings are useful if the equivalent problem can be exactly solved. A second major challenge to theorists is to develop an understanding of the behavior of statistical systems driven far from equilibrium, and my group has an on-going effort in this area. We are currently studying the behavior of a system that is both structurally disordered and far from equilibrium.