The Dynamical Cluster Approximation

The DCA is a general approach for the theory of correlated and disordered lattice systems which maps the lattice onto a self consistently embedded periodic cluster. When the cluster size is one the mean field solution is recovered (DMFT or CPA), and as the cluster size increases non-local corrections are systematically incorporated. A variety of methods may be used to solve the cluster problem. The DCA has been used to study a variety of systems, including the cuprates, dilute magnetic semiconductors and carbon nanotubes. The DCA formalism, comparison with other cluster methods, and these applications will be reviewed.