Titlebook: Introduction to the Functional Renormalization Group; Peter Kopietz,Lorenz Bartosch,Florian Schütz Book 2010 Springer-Verlag Berlin Heidel

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Fermionic Functional Renormalization Group a discussion of the rescaling problem for normal fermions, which leads to a nonperturbative definition of the Fermi surface. Finally, we discuss in Sect. 10.5 the one-loop patching approximation and present numerical results for the square-lattice Hubbard model.

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Field-Theoretical Renormalization Groupmethod.. More detailed introductions can be found in the authoritative book by Zinn-Justin (2002) or in many other textbooks on quantum field theory such as (Sterman 1993, Peskin and Schroeder 1995, Zee 2003).

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Phase Transitions and the Scaling Hypothesisefine the critical exponents, and discuss the relevant scaling laws. For a more detailed discussion of these topics, we refer the reader to other reviews and textbooks (Fisher 1983, Binney et al. 1992, Goldenfeld 1992, Ivanchenko and Lisyansky 1995, Cardy 1996, McComb 2004, Kardar 2007).

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Exact FRG Flow Equations that fluctuations with wave vectors (or energies) below the cutoff scale are suppressed, while the short-wavelength, high-energy fluctuations are not modified. There is considerable freedom in the implementation of the cutoff procedure, as will be discussed in Sect. 7.1.

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Vertex Expansion is based on a suitable truncation of the hierarchy of integro-differential equations for the vertices. This vertex expansion approach was pioneered by Morris (1994) and has been extensively used in the condensed matter community.

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Derivative Expansionradients of the fields . seems reasonable. Such an expansion is justified by noting that, although the true generating functional of the irreducible vertices . can contain nonanalyticities, the flowing . is analytic for any finite value of the cutoff ..