Global flow of the Higgs potential in a Yukawa model

Borchardt, Julia; Gies, Holger; Sondenheimer, René

doi:10.1140/epjc/s10052-016-4300-9

Cited by 43 publications

(75 citation statements)

References 107 publications

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“…In practice, this suggests to compute the IR flow approximately in terms of a simple polynomial expansion of the potential. In fact, the reliability of such an expansion for a description of Fermi scale observables has been verified for a variety of standard-modellike (gauged)-Higgs-Yukawa models in [86][87][88][89][90].…”

Section: Ir Flows and Mass Spectrummentioning

confidence: 97%

Non-Abelian Higgs models: Paving the way for asymptotic freedom

Gies¹,

Zambelli²

2017

Phys. Rev. D

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Asymptotically free renormalization group trajectories can be constructed in nonabelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of simple low-order perturbation theory, effective field theory, as well as modern functional renormalization group equations. We construct a family of explicit scaling solutions using a controlled weak-coupling expansion in the ultraviolet, and obtain a standard Wilsonian RG relevance classification of perturbations about scaling solutions. We obtain global information about the quasi-fixed function for the scalar potential by means of analytic asymptotic expansions and numerical shooting methods. Further analytical evidence for such asymptotically free theories is provided in the large-N limit. We estimate the long-range properties of these theories, and identify initial/boundary conditions giving rise to a conventional Higgs phase.

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Section: Ir Flows and Mass Spectrummentioning

confidence: 97%

Non-Abelian Higgs models: Paving the way for asymptotic freedom

Gies¹,

Zambelli²

2017

Phys. Rev. D

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“…64, the fixed point structure of the O(N ) ⊕ O(M )-model was studied pseudo-spectrally between two and three dimensions. Lately, the method was extended to the integration of flows 65,66 . In contrast to the situation in perturbation theory, not much is known about the convergence properties of approximations to the exact renormalisation group from first principles.…”

Section: Introductionmentioning

confidence: 99%

Ising and Gross-Neveu model in next-to-leading order

Knorr

2016

Phys. Rev. B

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We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalisation group. Their critical behaviour is of special interest in condensed matter systems, in particular graphene. To derive the beta functions, we make extensive use of computer algebra. The resulting flow equations were solved with pseudo-spectral methods to guarantee high accuracy. New estimates on critical quantities for both the Ising and the Gross-Neveu model are provided. For the Ising model, the estimates agree with earlier renormalisation group studies of the same level of approximation. By contrast, the approximation for the Gross-Neveu model retains many more operators than all earlier studies. For two Dirac fermions, the results agree with both lattice and large-N f calculations, but for a single flavour, different methods disagree quantitatively, and further studies are necessary.

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“…Then we investigate quantum mechanical examples with bounded or non-analytic potentials, as exact results from directly solving the Schrödinger equation can be calculated and compared to. Further applications of the method can be found in [53,54]. We emphasise that the methods presented here are heavily used in other contexts [55,56], as e.g.…”

Section: Introductionmentioning

confidence: 99%

Solving functional flow equations with pseudospectral methods

Borchardt

Knorr

2016

Phys. Rev. D

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We apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations [1]. The advantages of our method are illustrated with the help of two classes of models: first, to make contact with literature, we investigate flows of the O(N )-model in 3 dimensions, for N = 1, 4 and in the large N limit. For the case of a fractal dimension, d = 2.4, and N = 1, we follow the flow along a separatrix from a multicritical fixed point to the Wilson-Fisher fixed point over almost 13 orders of magnitude. As a second example, we consider flows of bounded quantum-mechanical potentials, which can be considered as a toy model for Higgs inflation. Such flows pose substantial numerical difficulties, and represent a perfect test bed to exemplify the power of pseudo-spectral methods.

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Global flow of the Higgs potential in a Yukawa model

Cited by 43 publications

References 107 publications

Non-Abelian Higgs models: Paving the way for asymptotic freedom

Non-Abelian Higgs models: Paving the way for asymptotic freedom

Ising and Gross-Neveu model in next-to-leading order

Solving functional flow equations with pseudospectral methods

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