M\'etodo de BPHZ para Pontos de Lifshitz m-Axiais Anisotr\'opicos
  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. 
Emanuel V. Souza
cond-mat.other cond-mat.stat-mech hep-th