On the Large-Distance Behavior of Correlations for a Hierarchical N-Component Classical Vector Model in Three Dimensions

We consider the correlation functions for a hierarchical N-component classical vector model in three dimensions. For N = ∞, we find explicitly the eigenvalues and global eigenfunctions of the linearized renormalization group transformation. In a very direct way, this yields the correlation functions for the N = ∞ model. In particular, we check that the two-point function has canonical decay.