Importance of the massive modes in the renormalization group 2+ε dimension

We study the renormalization group for the non-linear σ-models Sn-1, R P2 and Vn,2 in the limit d = 2+ε, keeping all the modes, massive and massless. The local potential approximation is used for the renormalization group. In a first step, the Sn-1 models (usually called O(n) models) are solved in this approximation. Then, we study the R P2 and Vn,2 models. We find the fixed points in the flow and the corresponding critical exponents. Due to the massive modes, the critical exponents differ at order ε2 when compared to the one found in the usual 2+ε expansion. In particular, various models with the same tangent space (which have an identical critical behavior in the usual computations) differ at order ε2. ((orig.))