  Starting from the canonical ensemble over the space of pure quantum states,
we obtain an integral representation for the partition function. This is used
to calculate the magnetisation of a system of N spin-1/2 particles. The results
suggest the existence of a new type of first order phase transition that occurs
at zero temperature in the absence of spin-spin interactions. The transition
arises as a consequence of quantum entanglement. The effects of internal
interactions are analysed and the behaviour of the magnetic susceptibility for
a small number of interacting spins is determined.
