Longitudinal and Transverse Correlation Functions in the ϕ4 Model below and near the Critical Point

We have extended our method of grouping Feynman diagrams (GFD theory) to study the transverse and longitudinal correlation functions G⊥(k) and G‖(k) in ϕ4 model below the critical point (T < Tc) in the presence of an infinitesimal external field. Our method allows a qualitative analysis without cutting the perturbation series. The long-wave limit k → 0 has been studied at T < Tc, showing that G⊥(k) a k−λ ⊥ and G‖(k) b k−λ ‖ with exponents d/2 < λ ⊥ < 2 and λ ‖ = 2λ⊥−d are the physical solutions of our equations at the spatial dimensionality 2 < d < 4, which coincides with the asymptotic solution at T → Tc as well as with a nonperturbative renormalization group (RG) analysis provided in our paper. This has been confirmed also by recent Monte Carlo simulations. The exponents as well as the ratio bM2/a2 (where M is magnetization) are universal. The results of the perturbative RG method are reproduced by formally setting λ ⊥ = 2, although our analysis yields λ ⊥ < 2. Subject Index: 370 Phase transitions and critical phenomena are widely investigated fields in physics and natural sciences.1)–6) This paper is devoted to the further development of ou