Wegner-Houghton equation and derivative expansion

Alfio Bonanno, Vincenzo Branchina, Herve Mohrbach, Dario Zappalà
1999 Physical Review D, Particles and fields  
We study the derivative expansion for the effective action in the framework of the Exact Renormalization Group for a single component scalar theory. By truncating the expansion to the first two terms, the potential U_k and the kinetic coefficient Z_k, our analysis suggests that a set of coupled differential equations for these two functions can be established under certain smoothness conditions for the background field and that sharp and smooth cut-off give the same result. In addition we find
more » ... hat, differently from the case of the potential, a further expansion is needed to obtain the differential equation for Z_k, according to the relative weight between the kinetic and the potential terms. As a result, two different approximations to the Z_k equation are obtained. Finally a numerical analysis of the coupled equations 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.
doi:10.1103/physrevd.60.065009 fatcat:rsmg77xqjvh7hh5vekue2oi5oa