Wegner-Houghton equation and derivative expansion - art. no. 065009

We study the derivative expansion for the effective action in the framework of the exact renormalization,group for a single component scalar theory. B y truncating the expansion to the first two terms, the potential U-k and th e kinetic coefficient Z(k), our analysis suggests that a set of coupled dif ferential equations for these two functions can be established under certai n smoothness conditions for the background field and that sharp and smooth cutoff give the same result. In addition we find that, differently from the case of the potential, a further expansion is needed to obtain the differe ntial equation for Z(k), according to the relative weight between the kinet ic and the potential terms. As a result, two different approximations to th e Z(k) equation are obtained. Finally a numerical analysis of the coupled e quations for U-k and Z(k) is performed at the non-Gaussian fixed point in D < 4 dimensions to determine the anomalous dimension of the field. [S0556-2 821(99)00316-1].