Critical nature of ideal Bose-Einstein condensation: Similarity with Yang-Lee theory of phase transition

Abstract

It is found that the singularity of the thermodynamic potential of an ideal Bose gas is connected with the physical root ${z}_{0}=1$ of the inverse of the grand partition function. The critical nature is determined solely by the behavior of the root distribution of the inverse of the grand partition function near ${z}_{0}=1$. This is quite similar to the situation of phase transition described by Yang-Lee theory.