Two-particle irreducible finite temperature effective potential of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>linear sigma model in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>dimensions at next-to-leading order of<mml:math xmlns:mml="http://www.w3.org/1998/Math/Mat

Baacke, Juergen; Michalski, Stefan

doi:10.1103/physrevd.70.085002

Cited by 10 publications

(5 citation statements)

References 41 publications

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“…On a practical level, the equations that we have obtained provide an alternative method to solve the gap equation at κ = 0 via a smooth integration of fluctuations in successive momentum-shells controlled by the regulating scale κ. This is in contrast to standard methods, such as those based on iterations of the gap and BS equations, that may exhibit instabilities and do not always converge (of course other methods exist to tame such instabilities [51,52]). On a more formal level, the flow equations provide much insight into the renormalization of Φ-derivable approximations, while opening the way to extensions that do not hinder their renormalizability.…”

Section: Initial Conditionsmentioning

confidence: 92%

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Functional renormalization group and 2PI effective action formalism

Blaizot,

Pawlowski,

Reinosa

2021

Preprint

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We combine two non-perturbative approaches, one based on the two-particle-irreducible (2PI) action, the other on the functional renormalization group (fRG), in an effort to develop new non-perturbative approximations for the field theoretical description of strongly coupled systems. In particular, we exploit the exact 2PI relations between the two-point and four-point functions in order to truncate the infinite hierarchy of equations of the functional renormalization group. The truncation is "exact" in two ways. First, the solution of the resulting flow equation is independent of the choice of the regulator. Second, this solution coincides with that of the 2PI equations for the two-point and the four-point functions, for any selection of two-skeleton diagrams characterizing a so-called Φ-derivable approximation. The transformation of the equations of the 2PI formalism into flow equations offers new ways to solve these equations in practice, and provides new insight on certain aspects of their renormalization. It also opens the possibility to develop approximation schemes going beyond the strict Φ-derivable ones, as well as new truncation schemes for the fRG hierarchy.

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Section: Initial Conditionsmentioning

confidence: 92%

“…where the one-loop integral J κ (p) is defined in Eq. (52). Since Γ (4,1) is made of one-loop contributions, there is only an overall divergence in Eq.…”

Section: Diagrammatic Form Of the Countertermsmentioning

confidence: 99%

Functional renormalization group and 2PI effective action formalism

Blaizot,

Pawlowski,

Reinosa

2021

Preprint

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“…One important ingredient in solving iteratively a selfconsistent equation is the so-called under-relaxation method, which is meant to extend the domain of convergence of the iterative method and can be applied to the (inverse) propagator, as in [23,26], or to the selfenergy, as in [6,27]. Technically the method amounts to using at ith order of the iteration a weighted average of the (i − 1)th and ith quantities, with some parameter α < 1.…”

Section: A Solving the Equationsmentioning

confidence: 99%

The O(N)-model within the Phi-derivable expansion to order lambda^2: on the existence, UV and IR sensitivity of the solutions to self-consistent equations

Markó,

Reinosa,

Szép

2015

Preprint

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We discuss various aspects of the O(N )-model in the vacuum and at finite temperature within the Φ-derivable expansion scheme to order λ 2 . In continuation of an earlier work, we look for a physical parametrization in the N = 4 case that allows us to accommodate the lightest mesons. Using zero-momentum curvature masses to approximate the physical masses, we find that, in the parameter range where a relatively large sigma mass is obtained, the scale of the Landau pole is lower compared to that obtained in the two-loop truncation. This jeopardizes the insensitivity of the observables to the ultraviolet regulator and could hinder the predictivity of the model. Both in the N = 1 and N = 4 cases, we also find that, when approaching the chiral limit, the (iterative) solution to the Φ-derivable equations is lost in an interval around the would-be transition temperature. In particular, it is not possible to conclude at this order of truncation on the order of the transition in the chiral limit. Because the same issue could be present in other approaches, we investigate it thoroughly by considering a localized version of the Φ-derivable equations, whose solution displays the same qualitative features, but allows for a more analytical understanding of the problem. In particular, our analysis reveals the existence of unphysical branches of solutions which can coalesce with the physical one at some temperatures, with the effect of opening up a gap in the admissible values for the condensate. Depending on its rate of growth with the temperature, this gap can eventually engulf the physical solution.

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“…The large-N limit in O(N ) scalar theories provides a simple nonperturbative approach which captures nontrivial IR physics in flat space-time [27,28,[42][43][44]. Recently this approach has been applied in de Sitter space with interesting results [31,33].…”

Section: Introductionmentioning

confidence: 99%

Nonperturbative resummation of de Sitter infrared logarithms in the large-Nlimit

Serreau¹,

Renaud²

2013

Phys. Rev. D

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We study the O(N ) scalar field theory with quartic self-coupling in de Sitter space. When the field is light in units of the expansion rate, perturbative methods break down at very low momenta due to large infrared logarithmic terms. Using the nonperturbative large-N limit, we compute the four-point vertex function in the deep infrared regime. The resummation of an infinite series of perturbative (bubble) diagrams leads to a modified power law which is analogous to the generation of an anomalous dimension in critical phenomena. We discuss in detail the role of high momentum (subhorizon) modes, including the issue of renormalization, and show that they influence the dynamics of infrared (superhorizon) modes only through a constant renormalization factor. This provides an explicit example of effective decoupling between high and low energy physics in an expanding space-time.

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Two-particle irreducible finite temperature effective potential of theO(N)linear sigma model in1+1dimensions at next-to-leading order of
Juergen Baacke
¹
,
Stefan Michalski
²

Cited by 10 publications

References 41 publications

Functional renormalization group and 2PI effective action formalism

Functional renormalization group and 2PI effective action formalism

The O(N)-model within the Phi-derivable expansion to order lambda^2: on the existence, UV and IR sensitivity of the solutions to self-consistent equations

Nonperturbative resummation of de Sitter infrared logarithms in the large-Nlimit

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Two-particle irreducible finite temperature effective potential of theO(N)linear sigma model in1+1dimensions at next-to-leading order ofJuergen Baacke1, Stefan Michalski2

Cited by 10 publications

References 41 publications

Functional renormalization group and 2PI effective action formalism

Functional renormalization group and 2PI effective action formalism

The O(N)-model within the Phi-derivable expansion to order lambda^2: on the existence, UV and IR sensitivity of the solutions to self-consistent equations

Nonperturbative resummation of de Sitter infrared logarithms in the large-Nlimit

Contact Info

Product

Resources

About

Two-particle irreducible finite temperature effective potential of theO(N)linear sigma model in1+1dimensions at next-to-leading order of
Juergen Baacke
¹
,
Stefan Michalski
²