Critical (φ 4)3, Ǫ

The Euclidean (φ)3, ǫ model in R 3 corresponds to a perturbation by a φ interaction of a Gaussian measure on scalar fields with a covariance depending on a real parameter ε in the range 0 ≤ ε ≤ 1. For ε = 1 one recovers the covariance of a massless scalar field in R. For ε = 0 φ is a marginal interaction. For 0 ≤ ε < 1 the covariance continues to be Osterwalder-Schrader and pointwise positive. After introducing cutoffs we prove that for ε > 0, sufficiently small, there exists a non-gaussian fixed point ( with one unstable direction) of the Renormalization Group iterations. These iterations converge to the fixed point on its stable (critical) manifold which is constructed. ∗ Partially supported by NSERC of Canada ∗∗ Laboratoire Associé au CNRS, UMR 5825 ∗∗∗ Partially supported by CNR, G.N.F.M. and MURST 1/febbraio/2008 [1] 0:1