GRADIENT FLOWS FROM AN APPROXIMATION TO THE EXACT RENORMALIZATION-GROUP

Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in 2<d<4. The standard upper critical dimensions d(k)=2k/(k-1), k=2, 3, 4, ... appear naturally encoded in our formalism, and for dimensions smaller but very close to d(k) our results match the epsilon-expansion. Within the coupling constant subspace of mass and quartic couplings and for any d, we find a gradient flow with two fixed points determined by a positive-definite metric and a c-function which is monotonically decreasing along the flow.