  We discuss some recent results connected with the properties of temperature
states of quantum disordered systems. This analysis falls within the natural
framework of operator algebras. Among the results quoted here, we recall some
ergodic and spectral properties of KMS states, the possibility of defining the
chemical potential independently of the disorder, and finally the question of
the Gibbsianess for KMS states. This analysis can be considered as a step
towards fully understanding the very complicated structure of the set of
temperature states of quantum spin glasses, and its connection with the
breakdown of the symmetry for replicas.
