  The perturbative approach to nonlinear Sigma models and the associated
renormalization group flow are discussed within the framework of Euclidean
algebraic quantum field theory and of the principle of general local
covariance. In particular we show in an Euclidean setting how to define Wick
ordered powers of the underlying quantum fields and we classify the freedom in
such procedure by extending to this setting a recent construction of Khavkine,
Melati and Moretti for vector valued free fields. As a by-product of such
classification, we prove that, at first order in perturbation theory, the
renormalization group flow of the nonlinear Sigma model is the Ricci flow.
