Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

Defenu, Nicoló; Mati, P.; Márián, I. G.; Nándori, I.; Trombettoni, Andrea

doi:10.1007/jhep05(2015)141

Cited by 24 publications

(32 citation statements)

References 65 publications

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“…Note that this definition is compatible with usual truncations in the symmetric phase, that is with derivative and mean field expansion considered in the literature [84]- [85]. Moreover, in non-symmetric phase, a dependence of Z(s) on the means fields M andM is expected.…”

Section: Definition 25supporting

confidence: 70%

Nonperturbative renormalization group beyond the melonic sector: The effective vertex expansion method for group fields theories

2018

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Tensor models admit the large N limit dominated by the graphs called melons. The melons are caracterized by the Gurau number = 0 and the amplitude of the Feynman graphs are proportional to N − . Other leading order contributions i.e.> 0 called pseudomelons can be taken into account in the renormalization program. The following paper deals with the renormalization group for a U (1)-tensorial group field theory model taking into account these two sectors (melon and pseudo-melon). It generalizes a recent work [arXiv:1803.09902], in which only the melonic sector have been studied. Using the power counting theorem the divergent graphs of the model are identified. Also, the effective vertex expansion is used to generate in detail the combinatorial analysis of these two leading order sectors. We obtained the structure equations, that help to improve the truncation in the Wetterich equation. The set of Ward-Takahashi identities is derived and their compactibility along the flow provides a non-trivial constraints in the approximation shemes. In the symmetric phase the Wetterich flow equation is given and the numerical solution is studied. 1 vincent.lahoche@cea.fr 2 dine.ousmanesamary@cipma.uac.bj An important notion for tensorial Feynman diagrams is the notion of faces, whose we recall in the following definition:Definition 2 A face is defined as a maximal and bicolored connected subset of lines, necessarily including the color 0. We distinguish two cases:• The closed or internal faces, when the bicolored connected set correspond to a cycle.3 Strictly speaking the term "quantum" is abusive, we should talk about statistical model, or quantum field theory in the euclidean time.

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Section: Definition 25supporting

confidence: 70%

Nonperturbative renormalization group beyond the melonic sector: The effective vertex expansion method for group fields theories

2018

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“…However, our conclusions are based on the behavior of the effective potential rather than on a specific value of a physically relevant quantity as a critical exponent. We thus expect them to be solid with respect to this issue [ 62 , 63 , 64 , 72 , 72 ].…”

Section: Concluding Remarks and Open Issuesmentioning

confidence: 99%

Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra I: Matricial Data

Lahoche

Samary

Tamaazousti

2021

Entropy

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Renormalization group techniques are widely used in modern physics to describe the relevant low energy aspects of systems involving a large number of degrees of freedom. Those techniques are thus expected to be a powerful tool to address open issues in data analysis when datasets are highly correlated. Signal detection and recognition for a covariance matrix having a nearly continuous spectra is currently one of these opened issues. First, investigations in this direction have been proposed in recent investigations from an analogy between coarse-graining and principal component analysis (PCA), regarding separation of sampling noise modes as a UV cut-off for small eigenvalues of the covariance matrix. The field theoretical framework proposed in this paper is a synthesis of these complementary point of views, aiming to be a general and operational framework, both for theoretical investigations and for experimental detection. Our investigations focus on signal detection. They exhibit numerical investigations in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold.

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“…We get β m (p) = 0 = β 41 (p) = 0. Then the constraint (79) implies that at the point p we get ηλ 41 1 −λ 41 π 2 (1 +m 2 ) 2 (p) = 0.…”

Section: Convenient Search Of the Ward Identitiesmentioning

confidence: 99%

Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory

Lahoche

Samary

2019

Universe

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This manuscript aims at giving new advances on the functional renormalization group applied to the tensorial group field theory. It is based on a series of our three papers [arXiv:1803.09902], [arXiv:1809.00247] and [arXiv:1809.06081]. We consider the polynomial Abelian U (1) d models without closure constraint. More specifically, we discuss the case of the quartic melonic interaction. We present a new approach, namely the effective vertex expansion method, to solve the exact Wetterich flow equation, and investigate the resulting flow equations, specially regarding the existence of non-Gaussian fixed points for their connection with phase transitions. To complete this method, we consider a non-trivial constraint arising from the Ward-Takahashi identities, and discuss the disappearance of the global non-trivial fixed points taking into account this constraint. Finally, we argue in favor of an alternative scenario involving a first order phase transition into the reduced phase space given by the Ward constraint.

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Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

Cited by 24 publications

References 65 publications

Nonperturbative renormalization group beyond the melonic sector: The effective vertex expansion method for group fields theories

Nonperturbative renormalization group beyond the melonic sector: The effective vertex expansion method for group fields theories

Field Theoretical Approach for Signal Detection in Nearly Continuous Positive Spectra I: Matricial Data

Progress in Solving the Nonperturbative Renormalization Group for Tensorial Group Field Theory

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