  In this work we investigate the critical behavior of physical systems with
competing interactions that present points Lifshitz m-axial. For this study we
used the techniques of Quantum Field Theory with Massive Scalar interactions of
type {\lambda}{\phi}^4 in order to obtain a perturbative expansion for the
two-point vertex part up to the 3-loop order and four-point vertex function up
to 2-loop level. These vertex functions were regularized using the method of
dimensional regularization and renormalized using the minimal subtraction of
dimensional poles method.In particular, counterterms have been added to the
original Lagrangian, which is the main feature of the method BPHZ
(Bogoliubov-Parasiuk-Hepp-Zimmermann). Through the renormalization group ideas,
we defined the Wilson functions which shall produce nontrivial fixed points,
and from these functions and fixed points, we calculate the anisotropic
critical exponents {\eta}_{\tau}, to the order of three in number loops, and
{\nu}_{\tau} to the number of two in order loops, which characterize the
critical behavior of the Lifshitz type m-axial. The exponents calculated using
this technique are in perfect agreement with results obtained using other
methods, thus confirming the known and important hypothesis of universality.
