A new method of solution of the Wetterich equation and its applications

The known approximation schemes for the solution of the Wetterich exact renormalization group (RG) equation are critically reconsidered, and a new truncation scheme is proposed. In particular, the equations of the derivative expansion up to the partial differential (2)order for a scalar model are derived in a suitable form, clarifying the role of the off-diagonal terms in the matrix of functional derivatives. The natural domain of validity of the derivative expansion appears to be limited to small values ofq/kin the calculation of the critical two-point correlation function, depending on the wave-vector magnitudeqand the infrared cut-off scalek. The new approximation scheme has the advantage to be valid for anyq/k, and, therefore, it can be auspicious in many current and potential applications of the celebrated Wetterich equation and similar models. Contrary to the derivative expansion, derivatives are not truncated at a finite order in the new scheme. The RG flow equations in the first approximation of this new scheme are derived and approximately solved as an example. It is shown that the derivative expansion up to the partial differential (2)order is just the small-qapproximation of our new equations at the first order of truncation.