Longitudinal and Transverse Correlation Functions in the φ^4 Model below and near the Critical Point(Condensed Matter Physics)

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概要

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• We have extended our method of grouping Feynman diagrams (GFD theory) to study the transverse and longitudinal correlation functions G_⊥(κ) and G_‖(κ) in φ^4 model below the critical point (T<T_c) 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<T_c, showing that G_⊥(κ)≃ak^<-λ_⊥> and G_‖(κ)≃bk^<-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→T_c 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 bM^2/a^2 (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.

• 2010-10-25

著者

• KAUPUZS Jevgenijs

  Institute of Mathematics and Computer Science, University of Latvia

関連論文

• Longitudinal and Transverse Correlation Functions in the φ^4 Model below and near the Critical Point(Condensed Matter Physics)

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