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biblijskih citata iz Divkovićevih <i>Besjeda</i> s Kašićevom <i>Biblijom</i>

Horvat, Marijana; Radošević, Andrea

doi:10.34075/cs.55.1.2

Cited by 3 publications

(3 citation statements)

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“…We strongly believe that leveraging the vast existing knowledge for conservation laws in studies using the FRG and its (truncated) flow equations is very promising and the research in this direction should be continued and extended. All numerical numerical results as well as all figures in this work were obtained and designed using Mathematica [132] including the following Resource-Function(s) from the Wolfram Function Repository: PlotGrid [229], PolygonMarker [230], and MaTeXInstall [231]. The "Feynman" diagrams in Eqs.…”

Section: Discussionmentioning

confidence: 99%

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part I: The $O(N)$ model

Koenigstein,

Steil,

Wink

et al. 2021

Preprint

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The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this approach relies on the derivation of so-called flow equations, which describe the change of the quantum effective action under the variation of a coarse-graining parameter. In the present work, we discuss in detail a novel approach to solve such flow equations. This approach relies on the fact that RG equations can be rewritten such that they exhibit similarities with the conservation laws of fluid dynamics. This observation can be exploited in different ways. First of all, we show that this allows to employ powerful numerical techniques developed in the context of fluid dynamics to solve RG equations. In particular, it allows to reliably treat the emergence of non-analytic behavior in the RG flow of the effective action as it is expected to occur in studies of, e.g., spontaneous symmetry breaking. Second, the analogy between RG equations and fluid dynamics offers the opportunity to gain novel insights into RG flows and their interpretation in general, including the irreversibility of RG flows. We work out this connection in practice by applying it to zero-dimensional quantum-field theoretical models. The generalization to higherdimensional models is also discussed. Our findings are expected to help improving future FRG studies of quantum field theories in higher dimensions both on a qualitative and quantitative level.

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Section: Discussionmentioning

confidence: 99%

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part I: The $O(N)$ model

Koenigstein,

Steil,

Wink

et al. 2021

Preprint

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“…All numerical numerical results as well as all figures in this work were obtained and designed using Mathematica [134] including the following ResourceFunction(s) from the Wolfram Function Repository: PlotGrid [135], Poly-gonMarker [136], and MaTeXInstall [137].…”

Section: Discussionmentioning

confidence: 99%

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part III: Shock and rarefaction waves in RG flows reveal limitations of the $N \rightarrow \infty$ limit in $O(N)$-type models

Steil,

Koenigstein

2021

Preprint

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Using an O(N )-symmetric toy model QFT in zero space-time dimensions we discuss several aspects and limitations of the 1 N -expansion. We demonstrate, how slight modifications in a classical UV action can lead the 1 N -expansion astray and how the infinite-N limit may alter fundamental properties of a QFT. Thereby we present the problem of calculating correlation functions from two totally different perspectives: First, we explicitly analyze our model within an 1 N -saddle-point expansion and show its limitations. Secondly, we picture the same problem within the framework of the Functional Renormalization Group. Applying novel analogies between (F)RG flow equations and numerical fluid dynamics from parts I and II of this series of publications, we recast the calculation of expectation values of our toy model into solving a highly non-linear but exact advection(-diffusion) equation. In doing so, we find that the applicability of the 1 N -expansion to our toy model is linked to freezing shock waves in field space in the FRG-fluid dynamic picture, while the failure of the 1 N -expansion in this context is related to the annihilation of two opposing shock waves in field space.

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“…All plots in this work were produced using Mathematica [57] including the MaTeX package [58]. The manuscript was prepared with the support of GitHubCopilot [59].…”

Section: Acknowledgmentsmentioning

confidence: 99%

Detecting inhomogeneous chiral condensation from the bosonic two-point function in the (1 + 1)-dimensional Gross–Neveu model in the mean-field approximation*

Koenigstein¹,

Pannullo²,

Rechenberger³

et al. 2022

J. Phys. A: Math. Theor.

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The phase diagram of the (1 + 1)-dimensional Gross-Neveu model is reanalyzed for (non-)zero chemical potential and (non-)zero temperature within the mean-ﬁeld approximation. By investigating the momentum dependence of the bosonic two-point function, the well-known second-order phase transition from the ℤ2 symmetric phase to the so-called inhomogeneous phase is detected. In the latter phase the chiral condensate is periodically varying in space and translational invariance is broken. This work is a proof of concept study that conﬁrms that it is possible to correctly localize second-order phase transition lines between phases without condensation and phases of spatially inhomogeneous condensation via a stability analysis of the homogeneous phase. To complement other works relying on this technique, the stability analysis is explained in detail and its limitations and successes are discussed in context of the Gross-Neveu model. Additionally, we present explicit results for the bosonic wave-function renormalization in the mean-ﬁeld approximation, which is extracted analytically from the bosonic two-point function. We ﬁnd regions – a so-called moat regime – where the wave function renormalization is negative accompanying the inhomogeneous phase as expected.

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Usporedba biblijskih citata iz Divkovićevih Besjeda s Kašićevom Biblijom

Cited by 3 publications

References 0 publications

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part I: The $O(N)$ model

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part I: The $O(N)$ model

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases - Part III: Shock and rarefaction waves in RG flows reveal limitations of the $N \rightarrow \infty$ limit in $O(N)$-type models

Detecting inhomogeneous chiral condensation from the bosonic two-point function in the (1 + 1)-dimensional Gross–Neveu model in the mean-field approximation*

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