Pseudo-ɛ-Expansion and the Two-Dimensional Ising Model

Sokolov, A. I.

doi:10.1134/1.2131160

Cited by 17 publications

(18 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first 4(5) coefficients in ν −1 agree with the results obtained in ref. [17] ( [20]), providing a consistency check on the determination of our coefficients up to O(v 5 ). The remaining three coefficients are new.…”

Section: Discussionmentioning

confidence: 80%

Renormalization scheme dependence, RG flow, and Borel summability in ϕ4 theories in d<4

2019

View full text Add to dashboard Cite

Renormalization group (RG) and resummation techniques have been used in Ncomponent φ 4 theories at fixed dimensions below four to determine the presence of non-trivial IR fixed points and to compute the associated critical properties. Since the coupling constant is relevant in d < 4 dimensions, the RG is entirely governed by renormalization scheme-dependent terms. We show that the known proofs of the Borel summability of observables depend on the renormalization scheme and apply only in "minimal" ones, equivalent in d = 2 to an operatorial normal ordering prescription, where the β-function is trivial to all orders in perturbation theory. The presence of a non-trivial fixed point can be unambiguously established by considering a physical observable, like the mass gap, with no need of RG techniques. Focusing on the N = 1, d = 2 φ 4 theory, we define a one-parameter family of renormalization schemes where Borel summability is guaranteed and study the accuracy on the determination of the critical exponent ν as the scheme is varied. While the critical coupling shows a significant sensitivity on the scheme, the accuracy in ν is essentially constant. As by-product of our analysis, we improve the determination of ν obtained with RG methods by computing three more orders in perturbation theory.

show abstract

Section: Discussionmentioning

confidence: 80%

Renormalization scheme dependence, RG flow, and Borel summability in ϕ4 theories in d<4

2019

View full text Add to dashboard Cite

show abstract

“…19 in the paper of Le Guillou and Zinn-Justin [4]). The pseudo-expansion approach has been shown to be very efficient when used to estimate critical exponents and other universal quantities for various 3D and 2D systems [4,35,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57].…”

Section: Introductionmentioning

confidence: 99%

Effective potential of the three-dimensional Ising model: The pseudo- ϵ expansion study

2017

View full text Add to dashboard Cite

The ratios R 2k of renormalized coupling constants g 2k that enter the effective potential and smallfield equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar λφ 4 field theory (3D Ising model) within the pseudo-expansion approach. Pseudo-expansions for the critical values of g 6 , g 8 , g 10 , R 6 = g 6 /g 2 4 , R 8 = g 8 /g 3 4 and R 10 = g 10 /g 4 4 originating from the five-loop renormalization group (RG) series are derived. Pseudo-expansions for the sextic coupling have rapidly diminishing coefficients, so addressing Padé approximants yields proper numerical results. Use of Padé-Borel-Leroy and conformal mapping resummation techniques further improves the accuracy leading to the values R * 6 = 1.6488 and R * 6 = 1.6490 which are in a brilliant agreement with the result of advanced lattice calculations. For the octic coupling the numerical structure of the pseudo-expansions is less favorable. Nevertheless, the conform-Borel resummation gives R * 8 = 0.868, the number being close to the lattice estimate R * 8 = 0.871 and compatible with the result of 3D RG analysis R * 8 = 0.857. Pseudo-expansions for R * 10 and g * 10 are also found to have much smaller coefficients than those of the original RG series. They remain, however, fast growing and big enough to prevent obtaining fair numerical estimates.

show abstract

“…Below we apply the Padé-Borel-Leroy resummation technique which proved to be rather efficient when used to evaluate critical exponents on the base of corresponding pseudoexpansions [28,35,[38][39][40]. This technique employs the Borel-Leroy transformation of the original series…”

Section: Quarks-2016mentioning

confidence: 99%

“…To do this we address the pseudo-expansion approach which proved to be very efficient numerically when used to evaluate the critical exponents and other universal parameters of various 3D and 2D systems [27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Universal effective coupling constant ratios of 3D scalarϕ⁴field theory and pseudo-ϵexpansion

2016

Self Cite

View full text Add to dashboard Cite

Pseudo-ɛ-Expansion and the Two-Dimensional Ising Model

Cited by 17 publications

References 23 publications

Renormalization scheme dependence, RG flow, and Borel summability in ϕ4 theories in d<4

Renormalization scheme dependence, RG flow, and Borel summability in ϕ4 theories in d<4

Effective potential of the three-dimensional Ising model: The pseudo- ϵ expansion study

Universal effective coupling constant ratios of 3D scalarϕ⁴field theory and pseudo-ϵexpansion

Contact Info

Product

Resources

About

Pseudo-ɛ-Expansion and the Two-Dimensional Ising Model

Cited by 17 publications

References 23 publications

Renormalization scheme dependence, RG flow, and Borel summability in ϕ4 theories in d<4

Renormalization scheme dependence, RG flow, and Borel summability in ϕ4 theories in d<4

Effective potential of the three-dimensional Ising model: The pseudo- ϵ expansion study

Universal effective coupling constant ratios of 3D scalarϕ4field theory and pseudo-ϵexpansion

Contact Info

Product

Resources

About

Universal effective coupling constant ratios of 3D scalarϕ⁴field theory and pseudo-ϵexpansion