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## Interacting Fermi liquid in two dimensions at finite temperature, Part II: Renormalization

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Citations: | 17 - 9 self |

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158 | From Perturbative to Constructive Renormalization
- Rivasseau
- 1991
(Show Context)
Citation Context ...so called dangerous subgraphs, which means four-point and two-point quasi-local subgraphs. Remark that a subgraph is called quasilocal if all internal lines have energy higher than all external lines =-=[R]-=-. These contributions are decomposed into a renormalized part with improved power counting, and a localized part which in turn is absorbed into a flow of effective constants. To implement this renorma... |

54 |
Gallavotti G.: Perturbation theory of the Fermi surface in a quantum liquid. A general quasi particle formalism and one dimensional systems
- Benfatto
- 1990
(Show Context)
Citation Context ...quid bound into Cooper pairs and the metal becomes superconducting. During the last ten years a program has been designed to investigate rigorously this phenomenon by means of field theoretic methods =-=[BG]-=-[FT12][FMRT1-3][S1]. In particular the renormalization group of Wilson and 1followers has been extended to models with surface singularities such as the Fermi surface. The ultimate goal is to create ... |

44 |
forests and jungles: A botanical garden for cluster expansions
- Abdesselam, Rivasseau, et al.
- 1995
(Show Context)
Citation Context ...on as the final connected components are built. The result is a sum over forests, a forest being a set of disjoint trees. Like in [DR1] we use the ordered Brydges-Kennedy Taylor formula, which states =-=[AR1]-=- that for any smooth function H of the n(n − 1)/2 variables ul, l ∈ Pn = {(i, j)|i, j ∈ {1, .., n}, i ̸= j}, H|ul=1 = ∑ ⎛ ⎞ ⎛ ⎞ ∫ k∏ k∏ ∂ ⎝ dwq ⎠ ⎝ H⎠ (w F l (wq), l ∈ Pn) 0≤w1≤...≤wk≤1 q=1 ∂ulq o−F q... |

42 | An infinite volume expansion for many Fermions Green’s functions Helv
- Magnen, Trubowitz
- 1992
(Show Context)
Citation Context ...alysis around the Fermi surface. Renormalization group flows were studied perturbatively in the context of a spherical Fermi surface in [FT2]. A non perturbative study in 2 dimension was performed in =-=[FMRT1]-=-, but it was limited to so called “completely convergent graphs”. In this paper we rely heavily on the ideas introduced in [FMRT1], but we extend them to include non perturbative renormalization 2of ... |

38 |
Effective action for the Yukawa 2 quantum field Theory
- Lesniewski
- 1987
(Show Context)
Citation Context ...impulsions at a distance at most ΛT from the Fermi surface. Let’s see how propagators for tree and loop lines look like. 4 The first example of combining a tree expansion with a Gram bound appears in =-=[L]-=-. We thank G. Gallavotti and C. Wieczerkowski for pointing out this reference to us. 11Λ0 Λ(wn-1) Λ(w n-2 ) impulsions n n-1 Λ(w1) Λ T 0 links of the tree 1 positions Figure 2: Band structure II.4.1 ... |

27 |
la nature analytique des solutions des équations aux dérivées partielles. Premier mémoire.” Annales Scientifiques de l’École Normale Supérieure (3) 35
- Gevrey
- 1918
(Show Context)
Citation Context ...n f ∈ C ∞ (R d ) with compact support is in the Gevrey class of order s if there exist two constants A and µ such that ∀n ≥ 0, ||f (n) || 1 ≤ Aµ −n ( n ) ns e and its Fourier transform satisfies (see =-=[G]-=-): (II.10) ∀k ∈ R d | ˆ f(k)| ≤ Ae −s ( ) µ√d 1/s |k| (II.11) 7In short in the support of Cα(k) we have || ⃗ k| − 1| ≃ 1 √ α and k0 ≃ 1/ √ α, but they cannot be simultaneously much smaller. Remark th... |

26 |
The flow of an Electron-Phonon System to the Superconducting State, Helv. Phys. Acta 64213
- Feldman, Trubowitz
- 1991
(Show Context)
Citation Context ...bation theory. Our analysis relies on a renormalization group analysis around the Fermi surface. Renormalization group flows were studied perturbatively in the context of a spherical Fermi surface in =-=[FT2]-=-. A non perturbative study in 2 dimension was performed in [FMRT1], but it was limited to so called “completely convergent graphs”. In this paper we rely heavily on the ideas introduced in [FMRT1], bu... |

26 | Perturbation Theory for many fermion systems - Feldman, Trubowitz - 1990 |

20 | Trubowitz, Perturbation Theory around Non-nested Fermi Surfaces I. Keeping the Fermi Surface Fixed
- Feldman, Salmhofer, et al.
- 1996
(Show Context)
Citation Context ... program is well under way [FKST]. However this program requires to control rigorously the stability of a non-spherical Fermi surface under the renormalization group flow, a difficult technical issue =-=[FST]-=-; - one can study the Fermi liquid theory at finite temperature above the BCS transition temperature. A system of weakly interacting electrons has an obviously stable thermodynamic limit at high enoug... |

18 | Continuous renormalization for fermions and Fermi liquid theory
- Salmhofer
- 1998
(Show Context)
Citation Context ...le thermodynamic limit at high enough temperature, since the temperature acts as an infrared cutoff on the propagator in the field theory description of the model. In this point of view, advocated by =-=[S2]-=-, the non trivial theorem consists in showing that stability (i.e. summability of perturbation theory) holds for all temperatures higher than a certain critical temperature whose dependence in terms o... |

15 | An Intrisic 1/N Expansion for Many Fermion Systems, Europhys
- Magnen, Trubowitz
- 1993
(Show Context)
Citation Context ...perature of Fermions systems. A more difficult step is to glue this analysis to a kind of 1/N expansion and to a bosonic analysis to control the region at distance ∆BCS ≃ e −co/λ of the Fermi surface =-=[FMRT2]-=-. In two dimensions and finite temperature we cannot expect true symmetry breaking by the Mermin-Wagner theorem, but we can expect a Kosterlitz-Thouless phase for a two dimensional bosonic field in a ... |

14 | and V.Rivasseau, Continuous constructive fermionic renormalization
- Disertori
(Show Context)
Citation Context ...p scheme around the Fermi surface (an other idea advocated in [S1]). This scheme has been tested first in the simpler case of the Gross Neveu model (a field theory where there is no Fermi surface) in =-=[DR1]-=-. The next natural step in this program is to add the computation of coupling constants flows (i.e. renormalization of four point functions). This should be a rather straightforward extension of the m... |

10 | A Single Scale Infinite Volume Expansion for Three Dimensional Many Fermion Green’s Functions
- Magnen, Rivasseau
- 1995
(Show Context)
Citation Context ...e it isolates the constructive arguments from the computation of the renormalization group flow. We conjecture that the same theorem holds in three dimensions but have no proof until now (see however =-=[MR]-=- for a partial result in that direction). The rest of the paper is devoted to a proof of Theorem 1. III Further Expansion Steps III.1 Chains The decomposition into bands has a price, that is we have t... |

9 | Perturbation theory for Many Fermion - Feldman, Trubowitz - 1991 |

8 |
Explicit Fermionic Cluster Expansion
- Abdesselam, Rivasseau
- 1998
(Show Context)
Citation Context ...nal vertex vj for j = 1, ..., 2p (see [DR1]). Ω specifies for each tree line whether it comes from a ψ ¯ ψ or ¯ ψψ contraction. ε(T , Ω) is a global ± sign whose exact (inessential) value is given in =-=[AR2]-=-. Finally wT is defined by Λ(wT) = ΛT. Remark that wT = 0 if ΛT = Λ, i.e. if Λ ≥ √ 2πT, and wT > 0 otherwise. The bound Λ(wi) ≥ ΛT ∀i is due to (II.14-II.15). In the following, as we are interested in... |

8 |
Local existence of the Borel transform
- Calan, Rivasseau
- 1981
(Show Context)
Citation Context ... external line (L), and is no longer an external of Tℓ1 x (L) and once as external line of Tℓ2 x line of Tℓ0(L). This proves the lemma. x The following Lemma is an improved version of Lemmas B4-B5 in =-=[CR]-=- (see also Lemma III.6), adapted to this formalism of relative rather than total orderings. Lemma 10 Let CTS be a fixed Clustering Tree Structure of order n. We have ∑ ∑ 1 ∏ 1 T L n ! ℓ Nℓ(T , L) ≤ 4n... |

7 |
Identities and a Perturbative Analysis of a U(1) Goldstone Boson in a Many Fermion System, Helvetica Physica Acta 66
- Feldman, Magnen, et al.
- 1993
(Show Context)
Citation Context ...boson. The last part of the analysis consists therefore in the non-perturbative control of the infrared divergences associated to this Goldstone boson, using Ward identities at the constructive level =-=[FMRT3]-=-. Our result has quite a long proof, which we organized therefore in two main parts. In this paper we introduce the model and prove the analyticity of the “convergent contributions” to the vertex func... |

4 | Massless φ44 theory: Rigorous control of a renormalizable asymptotically free model - Gawedzki, Kupiainen - 1985 |

3 |
Improved Power Counting and Fermi
- Salmhofer
- 1998
(Show Context)
Citation Context ...per pairs and the metal becomes superconducting. During the last ten years a program has been designed to investigate rigorously this phenomenon by means of field theoretic methods [BG][FT12][FMRT1-3]=-=[S1]-=-. In particular the renormalization group of Wilson and 1followers has been extended to models with surface singularities such as the Fermi surface. The ultimate goal is to create a mathematically ri... |

3 | Construction of infrared φ44 by a phase space expansion - Feldman, Magnen, et al. - 1987 |

1 |
Continuous Constructive Fermionic Renormalization, preprint
- Disertori, Rivasseau
- 1998
(Show Context)
Citation Context ...p scheme around the Fermi surface (an other idea advocated in [S2]). This scheme has been tested first in the simpler case of the Gross Neveu model (a field theory where there is no Fermi surface) in =-=[DR1]-=-. The next natural step in this program is to add the computation of coupling constants flows (i.e. renormalization of four point functions). This should be a rather straightforward extension of the m... |