  We consider a disordered system obtained by coupling two mixed even-spin
models together. The chaos problem is concerned with the behavior of the
coupled system when the external parameters in the two models, such as,
temperature, disorder, or external field, are slightly different. It is
conjectured that the overlap between two independently sampled spin
configurations from, respectively, the Gibbs measures of the two models is
essentially concentrated around a constant under the coupled Gibbs measure.
Using the extended Guerra replica symmetry breaking bound together with a
recent development of controlling the overlap using the Ghirlanda-Guerra
identities as well as a new family of identities, we present rigorous results
on chaos in temperature. In addition, chaos in disorder and in external field
are addressed.
