Infrared Behavior of Systems With Goldstone Bosons

Anishetty, Ramesh; Basu, Rahul; Dass, N. D. Hari; Sharatchandra, H. S.

doi:10.1142/s0217751x99001615

Cited by 27 publications

(35 citation statements)

References 17 publications

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“…However for continuous symmetries in the ordered phase the presence of the Goldstone bosons has a strong impact on the infrared sector of the theory. In particular, according to the study of the susceptibility of the O(N)-symmetric theories (N > 1) [12,45,46] computation is performed in the LPA at λ = 0.13 and Λ = 10, in order to get closer to k = 0 and have a more accurate check on the behavior of V ′ k . In fact, in Fig.…”

Section: Field Renormalization In the Broken Phasementioning

confidence: 99%

Enhancement of field renormalization in scalar theories via functional renormalization group

Zappalà

2012

Phys. Rev. D

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The flow equations of the Functional Renormalization Group are applied to the O(N )-symmetric scalar theory, for N = 1 and N = 4, in four Euclidean dimensions, d = 4, to determine the effective potential and the renormalization function of the field in the broken phase. In our numerical analysis, the infrared limit, corresponding to the vanishing of the running momentum scale in the equations, is approached to obtain the physical values of the parameters by extrapolation. In the N = 4 theory a non-perturbatively large value of the physical renormalization of the longitudinal component of the field is observed. The dependence of the field renormalization on the UV cut-off and on the bare coupling is also investigated.

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Section: Field Renormalization In the Broken Phasementioning

confidence: 99%

Enhancement of field renormalization in scalar theories via functional renormalization group

Zappalà

2012

Phys. Rev. D

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“…G (k) = b k −λ at h = +0 and k → 0 (4) with certain exponents ρ, λ ⊥ , λ and the amplitudes a, b of the Fourier-transformed two-point correlation functions. In a series of theoretical works (e. g., [1][2][3][4][5][6][7]), it has been claimed that the exponents in (2) -(4) are exactly ρ = 1/2 at d = 3, λ ⊥ = 2 and λ = 4 − d, where d is the spatial dimensionality 2 < d < 4. These theoretical approaches are further referred here as the standard theory.…”

Section: Introductionmentioning

confidence: 99%

Correlation Functions, Universal Ratios and Goldstone Mode Singularities inn-Vector Models

Kaupužs

Melnik

Rimšāns

2014

Commun. comput. phys.

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Correlation functions in the O(n) models below the critical temperature are considered. Based on Monte Carlo (MC) data, we confirm the fact stated earlier by Engels and Vogt, that the transverse two-plane correlation function of the O(4) model for lattice sizes about L = 120 and small external fields h is very well described by a Gaussian approximation. However, we show that fits of not lower quality are provided by certain non-Gaussian approximation. We have also tested larger lattice sizes, up to L = 512. The Fourier-transformed transverse and longitudinal two-point correlation functions have Goldstone mode singularities in the thermodynamic limit at k → 0 and h = +0, i. e., G ⊥ (k) ≃ ak −λ ⊥ and G (k) ≃ bk −λ , respectively. Here a and b are the amplitudes, k =| k | is the magnitude of the wave vector k. The exponents λ ⊥ , λ and the ratio bM 2 /a 2 , where M is the spontaneous magnetization, are universal according to the GFD (grouping of Feynman diagrams) approach. Here we find that the universality follows also from the standard (Gaussian) theory, yielding bM 2 /a 2 = (n − 1)/16. Our MC estimates of this ratio are 0.06 ± 0.01 for n = 2, 0.17 ± 0.01 for n = 4 and 0.498 ± 0.010 for n = 10. According to these and our earlier MC results, the asymptotic behavior and Goldstone mode singularities are not exactly described by the standard theory. This is expected from the GFD theory. We have found appropriate analytic approximations for G ⊥ (k) and G (k), well fitting the simulation data for small k. We have used them to test the Patashinski-Pokrovski relation and have found that it holds approximately.

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“…Many theoretical works (see, e.g., [1][2][3][4][5] and references therein for the theoretical approaches further referred here as the standard theory), as well as numerical Monte Carlo (MC) studies [6][7][8][9][10] have been devoted to the investigation of the Goldstone mode ef- …”

Section: Introductionmentioning

confidence: 99%

Monte Carlo estimation of transverse and longitudinal correlation functions in the model

2010

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Infrared Behavior of Systems With Goldstone Bosons

Cited by 27 publications

References 17 publications

Enhancement of field renormalization in scalar theories via functional renormalization group

Enhancement of field renormalization in scalar theories via functional renormalization group

Correlation Functions, Universal Ratios and Goldstone Mode Singularities inn-Vector Models

Monte Carlo estimation of transverse and longitudinal correlation functions in the model

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