Renormalization Group Functions of CPN-1 Non-Linear  -Model and N-Component Scalar QED Model

The renormalization group functions of CPN-1 non-linear σ-model are studied in 2+ ε dimension by the ε-expansion. This CPN-1 model is shown to be related to the N-component scalar QED model for the large N case by the 1/N expansion. As applications in the statistical mechanics, superconductor and smectic A phase transitions are discussed.