Statistical mechanics of parafermi systems

Abstract

The statistical mechanics of a collection of parafermi harmonic oscillators considered as a canonical ensemble is examined. The factorization property of the corresponding partition function selects the representations of the parafermi ring allowed to furnish the energy levels of the oscillators. While the representations corresponding to Green's ansatz are in an obvious way perfect candidates, it is shown however that, contrary to expectations, they do not exhaust all the possibilities. The general conditions on the representations are given and special families of representations are outlined.