Renormalization-group fixed points of generaln-vector models

We make a general study of symmetry and stability of the fixed points of the quartic Hamiltonian of an $n$-component field (or order parameter) for $n\ne 4$. Simple proofs of known results are given. Among new results, we show that when it exists the stable fixed point is unique; we give some precision on its symmetry and on its attractor basin.