Phase separation in a polydisperse system

A system of molecules of high dimensionality and containing a large number of species (polydisperse) is studied. The species are labelled with a parameter; forces between molecules are repulsive, the effective repulsion between molecules of two given species increasing as the difference between the parameters for the two species increases. It is shown that for high enough density the homogeneous phase of such a system is unstable, in agreement with some recent computer simulation results suggesting instability of the homogeneous phase of a polydisperse system of discs. Some possible structures for the separated phases are also examined.