Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in O(N) models

Péli, Zoltán; Nagy, S.; Sailer, K.

doi:10.1140/epja/i2018-12385-9

Cited by 3 publications

(3 citation statements)

References 71 publications

(143 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is connected with the observation that the flow of the wave function renormalizations Z A does not exhibit the typical crossover region, 'the plateau' in the vicinity of the WF FP (see Sect. III C), just as in the case of the ordinary O(N ) models [36]. Moreover, using the parameters of the WF FP obtained in LPA1 as initial conditions and starting to solve the full set (60) of the flow equations in NLO1 towards the UV scale Λ, we could not arrive at Z A (Λ) = −1 (A =⊥, ) which are supposed to hold in the bare theory.…”

Section: B Characteristics Of the Fpsmentioning

confidence: 98%

“…= 0 with estimated initial values by means of computer algebraic algorithm. A detailed description of the application of both methods was given in [36]. The enlargement of the number of dimensions of the parameter space in the subsequent approximations LPA0 −→ LPA1 −→ NLO1 requires some additional refinements in the application of the fine-tuning and root-finder methods.…”

Section: Preliminary Numerical Studiesmentioning

confidence: 99%

“…The basic idea is that the dynamical symmetry breaking caused by the appearing of the periodic condensate is mimicked by explicit breaking of translation symmetry of the EAA. Similar approach is widely used in ordinary O(1) scalar models when the Z 2 symmetric double-well potential is approximated by its truncated Taylor-expansion around one of its mininima [34,35], and has also been successfully used in the case of the ordinary O(N ) scalar models, when spontaneous breaking of O(N ) symmetry has been partially mimicked by the inclusion of explicit symmetry breaking gradient terms into the EAA [36]. In a phase with a periodic condensate in the vacuum the EAA should have its minimum at the corresponding periodic field configuration.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modified renormalization group method applied to the $O(1)$ ghost model with periodic condensate

Péli¹,

Nagy²,

Sailer³

2018

Preprint

View full text Add to dashboard Cite

In order to discuss the occurrence of a periodic condensate in the Euclidean 3-dimensional ghost O(1) model, a modified version of the effective average action (EAA) renormalization group (RG) method is developed, called by us Fourier-Wetterich RG approach. It is proposed to start with an ansatz for the EAA, that contains terms, in addition to the usual ones, induced by the various Fourier-modes of the periodic condensate and to expand the EAA in functional Taylor-series around the periodic background. The RG flow equations are derived in the next-to-next-to-leading order of the gradient expansion (GE). No field-dependence of the derivative couplings have been taken into account and Z2 symmetry of the EAA is preserved. Preliminary numerical results have been obtained under various additional simplifying assumptions. The characteristics of the Wilson-Fisher fixed point and the phase structure of the model have been determined numerically in the local potential approximation and in the next-to-leading order of the GE, when the periodic condensate has been modelled by a single cosine mode in one spatial direction. From the preliminary results important information is gained on further possibilities to improve the proposed RG scheme.

show abstract

Section: B Characteristics Of the Fpsmentioning

confidence: 98%

Section: Preliminary Numerical Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modified renormalization group method applied to the $O(1)$ ghost model with periodic condensate

Péli¹,

Nagy²,

Sailer³

2018

Preprint

View full text Add to dashboard Cite

show abstract

Derivative expansion for computing critical exponents of O(N) symmetric models at next-to-next-to-leading order

Péli

2021

Phys. Rev. E

View full text Add to dashboard Cite

Phase structure of the Euclidean three-dimensional O(1) ghost model

Péli

Nagy

Sailer

2019

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

We have treated the Euclidean three-dimensional O(1) ghost model with a modified version of the effective average action (EAA) renormalization group (RG) method, developed by us. We call it Fourier–Wetterich RG approach and it is used to investigate the occurrence of a periodic condensate in terms of the functional RG. The modification involves additional terms in the ansatz of the EAA, corresponding to the Fourier-modes of the periodic condensate. The RG flow equations are derived keeping the terms up to the fourth order of the gradient expansion (GE), however the numerical calculations are conducted in the second order (or next-to-leading order, NLO) of the GE. The expansion of the flow equations around the nontrivial minimum of the local potential takes into account properly the vertices induced by the periodic condensate even if the wave function renormalization is set to be field-independent. The numerical analysis reveals several different phases with three multicritical points.

show abstract

Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in O(N) models

Cited by 3 publications

References 71 publications

Modified renormalization group method applied to the $O(1)$ ghost model with periodic condensate

Modified renormalization group method applied to the $O(1)$ ghost model with periodic condensate

Derivative expansion for computing critical exponents of O(N) symmetric models at next-to-next-to-leading order

Phase structure of the Euclidean three-dimensional O(1) ghost model

Contact Info

Product

Resources

About