2014/03/08 by Emanuel V. Souza, Souza, Emanuel V.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Other Condensed Matter (cond-mat.other) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.other #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.48550/arxiv.1403.1998
95 pages, 8 figures, Thesis Master, language Portuguese
arxiv created 2014/03/08 · openalex publication_date 2014/03/08 · arxiv updated 2014/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 λϕ4 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 ητ, to the order of three in number loops, and ντ 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.