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- W2493196055 abstract "This chapter discusses the generic O(N) non-linear σ-model. One property which plays an essential role is the UV asymptotic freedom of the σ-model in two dimensions. Some of its properties are expected to generalize to other asymptotically free models. In two dimensions, various fermion self-interacting models share this property. The symmetry which is then broken is the chiral symmetry which prevents explicit mass terms in the action. As in the case of the non-linear σ-model, IR divergences forbid the existence of a massless phase. One model of this kind can be defined in continuous dimensions, the Gross–Neveu (GN), a simpli cation of the Nambu–Jona-Lasinio model, which is studied in this chapter. It is renormalizable in two dimensions, and describes in perturbation theory only one phase, the phase with symmetry breaking. A model with the same symmetry can be identified, the Gross–Neveu–Yukawa (GNY) model which is renormalizable in four dimensions, and in which both phases can be reached already in the tree approximation. The study of these two models illustrates all the ideas and techniques developed in framework of the φ4 theory and the non-linear σ-models, that is RG equations near two and four dimensions, and large N expansion." @default.
- W2493196055 created "2016-08-23" @default.
- W2493196055 creator A5066570966 @default.
- W2493196055 date "2002-06-06" @default.
- W2493196055 modified "2023-09-26" @default.
- W2493196055 title "Phase Transitions Near Two Dimensions" @default.
- W2493196055 doi "https://doi.org/10.1093/acprof:oso/9780198509233.003.0031" @default.
- W2493196055 hasPublicationYear "2002" @default.
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