Critical phenomena from the two-particle irreducible<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:math>expansion

Alford, Mark; Berges, Jürgen; Cheyne, Jack M.

doi:10.1103/physrevd.70.125002

Cited by 36 publications

(57 citation statements)

References 29 publications

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“…Recently there has been interest in studying field theory using two-particle irreducible (2-PI) methods [1] in both finite temperature [2,3,4] and non-equilibrium situations [5,6,7,8,9,10,11,12,13,14]. The value of the 2-PI formalism for non-equilibrium problems is that it allows one to make approximations that go beyond the Hartree or large-N approximation without encountering the serious problems of secularity found in a straightforward expansion about the Hartree or leadingorder large-N approximation using the generating functional or, equivalently, the one-particle irreducible (1-PI) action [15].…”

Section: Introductionmentioning

confidence: 99%

Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation ofλϕ4field theory

2004

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In this paper we study the renormalization of the Schwinger-Dyson equations that arise in the auxiliary field formulation of the O(N) φ 4 field theory. The auxiliary field formulation allows a simple interpretation of the large-N expansion as a loop expansion of the generating functional in the auxiliary field χ, once the effective action is obtained by integrating over the φ fields. Our all orders result is then used to obtain finite renormalized Schwinger-Dyson equations based on truncation expansions which utilize the two-particle irreducible (2-PI) generating function formalism. We first do an all orders renormalization of the two-and three-point function equations in the vacuum sector. This result is then used to obtain explicitly finite and renormalization constant independent self-consistent S-D equations valid to order 1/N, in both 2+1 and 3+1 dimensions. We compare the results for the real and imaginary parts of the renormalized Green's functions with the related sunset approximation to the 2-PI equations discussed by Van Hees and Knoll, and comment on the importance of the Landau pole effect.

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Section: Introductionmentioning

confidence: 99%

Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation ofλϕ4field theory

2004

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“…Calculation of η In Ref. [7] the critical exponent η was calculated from the KB equation (36) at the critical point. Let us briefly review here how to obtain η, which is also necessary for the calculation of ν.…”

Section: Critical Exponents From 2pi Effective Actionmentioning

confidence: 99%

“…The authors are grateful to Jürgen Berges who drew their attention to Ref. [7] and stimulating discussions during the workshop. They also thank Hiroyuki Kawamura for discussions on renormalization issues.…”

Section: Acknowledgementsmentioning

confidence: 99%

Critical exponents from the two-particle irreducible1/Nexpansion

Saito

Fujii²,

Itakura³

et al. 2012

Phys. Rev. D

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We calculate the critical exponent ν in the 1/N expansion of the two-particle-irreducible (2PI) effective action for the O(N ) symmetric ϕ 4 model in three spatial dimensions. The exponent ν controls the behavior of a two-point function ϕϕ near the critical point T = Tc, but can be evaluated on the critical point T = Tc by the use of the vertex function Γ (2,1) . We derive a selfconsistent equation for Γ (2,1) within the 2PI effective action, and solve it by iteration in the 1/N expansion. At the next-to-leading order in the 1/N expansion, our result turns out to improve those obtained in the standard one-particle-irreducible calculation.

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“…The rules defining this expansion have been dicussed at length in Ref. [37,61,62]. We only recall here the main features of this expansion and we closely follows the notations employed in Ref.…”

Section: B Renormalization Groupmentioning

confidence: 99%

“…We only recall here the main features of this expansion and we closely follows the notations employed in Ref. [61,62].…”

Section: B Renormalization Groupmentioning

confidence: 99%

Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems

Mouhanna

Tarjus²

2010

Phys. Rev. E

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We investigate the relation between spontaneous and explicit replica symmetry breaking in the theory of disordered systems. On general ground, we prove the equivalence between the replicon operator associated with the stability of the replica symmetric solution in the standard replica scheme and the operator signaling a breakdown of the solution with analytic field dependence in a scheme in which replica symmetry is explicitly broken by applied sources. This opens the possibility to study, via the recently developed functional renormalization group, unresolved questions related to spontaneous replica symmetry breaking and spin-glass behavior in finite-dimensional disordered systems.

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Critical phenomena from the two-particle irreducible1/Nexpansion

Cited by 36 publications

References 29 publications

Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation ofλϕ4field theory

Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation ofλϕ4field theory

Critical exponents from the two-particle irreducible1/Nexpansion

Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems

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