O(N) models within the local potential approximation Original Research Article

Using the Wegner-Houghton equation, within the local potential approximation, we study critical properties of O(N) vector models. Fixed points, together with their critical exponents and eigenoperators, are obtained for a large set of values of N, including N = 0 and N → ∞. Polchinskiʹs equation is also treated. The peculiarities of the large N limit, where a line of Fixed Points at d = 2 + 2/n is present, are studied in detail. A derivation of the equation is presented together with its projection to zero-modes.