Nonlinear Models in2+εDimensions

1980/09/29 by Daniel Friedan · 17 citations
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Theoretical and Computational Physics #Physics #Nabla symbol #Riemannian manifold #Space (punctuation) #Coupling (piping) #Manifold (fluid mechanics) #Mathematical physics #Mathematical analysis #Omega #Quantum mechanics #Mathematics #Computer science #Materials science

paper · doi:10.1103/physrevlett.45.1057

openalex publication_date 1980/09/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A generalization of the nonlinear \ensuremathσ model is considered. The field takes values in a compact manifold M and the coupling is determined by a Riemannian metric on M. The model is renormalizable in 2+\ensuremathε dimensions, the renormalization group acting on the infinite-dimensional space of Riemannian metrics. Topological properties of the \ensuremathβ function and solutions of the fixed-point equation R_ij\ensuremath-\ensuremathαg_ij=\ensuremath∇_iv_j+\ensuremath∇_jv_i, \ensuremathα=\ifmmode±\else\textpm\fi1 or 0, are discussed.

Citations

• The renormalization group and the ε expansion
• Ordering, metastability and phase transitions in two-dimensional systems

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