2008
DOI: 10.1103/physrevb.77.024431
|View full text |Cite
|
Sign up to set email alerts
|

Calculations on the two-point function of theO(N)model

Abstract: The self-energy of the critical 3-dimensional O(N ) model is calculated. The analysis is performed in the context of the Non-Perturbative Renormalization Group, by exploiting an approximation which takes into account contributions of an infinite number of vertices. A very simple calculation yields the 2-point function in the whole range of momenta, from the UV Gaussian regime to the scaling one. Results are in good agreement with best estimates in the literature for any value of N in all momenta regimes. This … Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

0
25
0

Year Published

2009
2009
2022
2022

Publication Types

Select...
8

Relationship

1
7

Authors

Journals

citations
Cited by 24 publications
(25 citation statements)
references
References 58 publications
0
25
0
Order By: Relevance
“…Thus all propagators and vertices in (56) should be evaluated in the momentum and frequency range |q|, |p + q| k and |ω|/c, |ω + ω ν |/c k. In addition to the BMW approximation, we can therefore use the derivative expansion (30) of the vertices in the rhs of (56). This approximation has been shown be very reliable in classical models [41,44,45]. While we also expect a high degree of accuracy in the low-energy limit p → 0, the approximation is more questionable in the high-frequency limit.…”
Section: B Truncated Flow Equationsmentioning
confidence: 70%
See 1 more Smart Citation
“…Thus all propagators and vertices in (56) should be evaluated in the momentum and frequency range |q|, |p + q| k and |ω|/c, |ω + ω ν |/c k. In addition to the BMW approximation, we can therefore use the derivative expansion (30) of the vertices in the rhs of (56). This approximation has been shown be very reliable in classical models [41,44,45]. While we also expect a high degree of accuracy in the low-energy limit p → 0, the approximation is more questionable in the high-frequency limit.…”
Section: B Truncated Flow Equationsmentioning
confidence: 70%
“…If we set Γ C = 0 and p = (p, 0), we reproduce the flow equations of the classical O(2) model derived in Ref. [41].…”
Section: Bmw Equationsmentioning
confidence: 99%
“…For out-of-equilibrium problems, one formally proceeds as in equilibrium but with the presence of the additional response fields and with special care required to deal with the consequences of Itō's discretization and with causality issues, as stressed in detail in Refs. [38,47].…”
Section: The Nonperturbative Renormalization Groupmentioning
confidence: 99%
“…The expressions for the propagator (45), for the unique nonvanishing vertex (2,1) κ (44), and for the derivative of the regulator matrix (47) are then substituted into the NPRG equation (18) to get the flow equations for the (momentumand frequency-dependent) two-point functions (1,1) κ (ω, p) and (0,2) κ (ω, p). The flow equations for the functions f X κ are deduced following Eqs.…”
Section: Flow Equationsmentioning
confidence: 99%
“…approximations. The most appropriate nonperturbative approximation consists in expanding Γ k [φ] in powers of ∇φ [25][26][27][28][29][30][31][32][33][34]. At order two of the derivative expansion, Γ k reads:…”
mentioning
confidence: 99%