FIELD-THEORETIC APPROACH TO THE LIFSHITZ POINT

We study the renormalization of the field theory that describes the Li fshitz point (LP). Our motivation was an old controversy on the order- epsilon(2) values of critical exponents for this multicritical point. First we analyze the Green functions at the LP where same simplificati ons occur. The primitively divergent diagrams are identified and renor malization prescriptions that eliminate ultraviolet divergences to all orders of perturbation are found. The Green functions in the neighbor hood of the LP are expanded in terms of the Green functions calculated at the LP. This enables us to derive the renormalization-group equati on satisfied by the renormalized Green functions and by analyzing its solutions we find expressions for the critical exponents that hold to all orders of perturbation. Finally, we obtain generalized scaling rel ations for the exponents associated with the LP.