Five-loop renormalization group calculations in the gϕ4 theory

Chetyrkin, K.G.; Gorishny, S.G.; Larin, S.A.; Tkachov, F.V.

doi:10.1016/0370-2693(83)90324-6

Cited by 142 publications

(125 citation statements)

References 11 publications

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“…They reduce to the existing O(ǫ 5 ) ones for the O(N)-symmetric theory [38] in the proper limit. For the particular case n = m = 2 they agree, according to the exact mapping of Ref.…”

mentioning

confidence: 61%

Five-loop ϵ expansion for O(n)×O(m) spin models

Calabrese

Parruccini

2004

Nuclear Physics B

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We compute the Renormalization Group functions of a Landau-GinzburgWilson Hamiltonian with O(n)×O(m) symmetry up to five-loop in Minimal Subtraction scheme. The line n + (m, d), which limits the region of secondorder phase transition, is reconstructed in the framework of the ǫ = 4 − d expansion for generic values of m up to O(ǫ 5 ). For the physically interesting case of noncollinear but planar orderings (m = 2) we obtain n + (2, 3) = 6.1(6) by exploiting different resummation procedures. We substantiate this results re-analyzing six-loop fixed dimension series with pseudo-ǫ expansion, obtaining n + (2, 3) = 6.22(12). We also provide predictions for the critical exponents characterizing the second-order phase transition occurring for n > n + .

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“…They reduce to the existing O(ǫ 5 ) ones for the O(N)-symmetric theory [38] in the proper limit. For the particular case n = m = 2 they agree, according to the exact mapping of Ref.…”

mentioning

confidence: 61%

Five-loop ϵ expansion for O(n)×O(m) spin models

Calabrese

Parruccini

2004

Nuclear Physics B

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“…The expansion (14) has the same strong-coupling limit in D = 3 and D = 4 − ǫ dimensions, and it does not matter that µ = ζ (14) between u andū B , we obtain the bare coupling expansion of the renormalized square mass and fields:…”

Section: Exact Critical Exponents Up To Three Loopsmentioning

confidence: 99%

“…(14). Dividing this series byū B , we know that the leading power behaviour as u B → ∞ is −1 since u is supposed to go to the constant value u * : uū…”

Section: Critical Exponents From Two-loop Expansionsmentioning

confidence: 99%

“…With these conventions and notations, the renormalization constants in minimal subtraction are given up to three loops by [13][14][15] …”

Section: Model and Conventionsmentioning

confidence: 99%

“…In order to apply strong-coupling theory to the amplitude functions (85)-(88), we must reexpand them in powers of the bare couplingū B using (14) up to two loops. The strong-coupling limit is then given by the general expression (23), with ρ 2 /4 given by Eq.…”

Section: Amplitude Functions From Two-loop Expansionsmentioning

confidence: 99%

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Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory

Kleinert¹,

Bossche²

2001

Phys. Rev. E

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We use variational perturbation theory to calculate various universal amplitude ratios above and below Tc in minimally subtracted φ 4 -theory with N components in three dimensions. In order to best exhibit the method as a powerful alternative to Borel resummation techniques, we consider only to two-and three-loops expressions where our results are analytic expressions. For the critical exponents, we also extend existing analytic expressions for two loops to three loops.

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Feynman Amplitudes as Tempered Distributions

Smirnov¹

1985

Fortschr. Phys.

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Feynman amplitudes (FA) are analyzed with the help of the method which employs as much as possible the analogy between ultraviolet (UV) and infrared (IR) divergences and is based on a modified α‐representation. It is proved that an analytically and/or dimensionally regularized FA is a tempered distribution of external momenta and a meromorphic function of regularizing parameters with UV and IR poles. An absolutely convergent α‐representation of analytically and/or dimensionally regularized FA is derived in various analyticity domains. This representation is obtained from the α‐representation in the initial domain of convergence by inserting the operator which has the same structure as the R*‐operation that is a generalization of the dimensional renormalization.

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Five-loop renormalization group calculations in the gϕ4 theory

Cited by 142 publications

References 11 publications

Five-loop ϵ expansion for O(n)×O(m) spin models

Five-loop ϵ expansion for O(n)×O(m) spin models

Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory

Feynman Amplitudes as Tempered Distributions

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