Partition function of a disordered system

The Bloch density matrix of a disordered system can be expressed, at high temperatures, as a product arising from individual scattering centres. Using a property analogous to the idempotency of the corresponding Dirac matrix, it is shown how this approximation can be extended systematically to lower temperatures. Explicit forms are derived for the partition function of a random assembly and a liquid array with short range order, in terms of the single centre scattering properties and the structure factor.