Singularities in first-order phase transitions

Abstract

Several theories of phase transitions and their inter-relations have been criticized, focusing on the problem of whether z _c, the value of the fugacity corresponding to the point of condensation, is given by z _s, the smallest real positive singularity of the analytic function defined by the power series using volume-independent cluster integrals, or not. The present situation has been analysed and it is made clear that none of the existing theories can give the answer to this problem. Plausibility arguments for an affirmative or negative answer are discussed.