Precision calculation of critical exponents in the O(N) universality classes with the nonperturbative renormalization group

Polsi, Gonzalo De; Balog, Ivan; Tissier, Matthieu; Wschebor, Nicolás

doi:10.1103/physreve.101.042113

Cited by 94 publications

(182 citation statements)

References 90 publications

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“…which give the result η 6 = 0.0354512, η 7 = 0.0363063. Also our optimized result is η opt = 0.0367504 and all of these results lead to the predicted value ν = 0.03653(65) compared to Monte Carlo simulation result of η = 0.03627 (10), NPRG result η = 0.0361(11) [28] and conformal bootstrap calculation of η = 0.03631(3) [24] . For the correction to scaling exponent ω, the up to sevenloop order of perturbation series is given by Eq.…”

Section: Seven-loop Resummation Results For Ising-like Universality Csupporting

confidence: 65%

“…Thus our prediction for the ω exponent is ω = 0.82311 (50). NPRG method gives the result ω = 0.832(14) [28] while conformal bootstrap has the result ω = 0.8303(18) [24] and Monte Carlo simulations predicts the value ω = 0.832(6) [12]. Comparison with the predictions from more different methods is listed in Table 2.…”

Section: Seven-loop Resummation Results For Ising-like Universality Cmentioning

confidence: 70%

“…Accordingly, our prediction is ν = 0.62977 (22). To get an idea about how accurate this result is, we list here results from recent non-perturbative methods like the Monte Carlo simulations which gives the result ν = 0.63002(10) [12], the recent non-perturbative renormalization group (NPRG) method [28] which turns the result ν = 0.63012 (16) as well as the recent conformal bootstrap result ν = 0.62999 (5) in Ref. [24].…”

Section: Seven-loop Resummation Results For Ising-like Universality Cmentioning

confidence: 90%

“…[32] and five-loops (ε 5 ) from same reference. The recent results from the non-perturbative renormalization group (NPRG) method [28] For the exponent η, the suitable approximants are:…”

Section: Seven-loop Resummation Results For Ising-like Universality Cmentioning

confidence: 99%

“…Besides, bootstrapping the model in three dimensions has been accomplished recently and researchers succeeded to obtain precise results [22][23][24][25][26][27]. The nonperturbative renormalization group has been applied to the same model and gives accurate results too [28]. Apart from these nonperturbative methods, the oldest way to tackle the critical phenomena in QFT is resummation techniques applied to resum the divergent perturbation series associated with renormalization group (RG) functions of that model.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Critical exponents of the O(N)-symmetric $$\phi ^4$$ model from the $$\varepsilon ^7$$ hypergeometric-Meijer resummation

Shalaby

2021

Eur. Phys. J. C

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We extract the $$\varepsilon $$ ε -expansion from the recently obtained seven-loop g-expansion for the renormalization group functions of the O(N)-symmetric model. The different series obtained for the critical exponents $$\nu ,\ \omega $$ ν , ω and $$\eta $$ η have been resummed using our recently introduced hypergeometric-Meijer resummation algorithm. In three dimensions, very precise results have been obtained for all the critical exponents for $$N=0,1,2,3$$ N = 0 , 1 , 2 , 3 and 4. To shed light on the obvious improvement of the predictions at this order, we obtained the divergence of the specific heat critical exponent $$\alpha $$ α for the XY model. We found the result $$-0.0123(11)$$ - 0.0123 ( 11 ) which is compatible with the famous experimental result of $$-0.0127(3)$$ - 0.0127 ( 3 ) from the specific heat of zero gravity liquid helium superfluid transition while the six-loop Borel with conformal mapping resummation result in literature gives the value $$-0.007(3)$$ - 0.007 ( 3 ) . For the challenging case of resummation of the $$\varepsilon $$ ε -expansion series in two dimensions, we showed that our resummation results reflect a significant improvement to the previous six-loop resummation predictions.

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Section: Seven-loop Resummation Results For Ising-like Universality Csupporting

confidence: 65%

Section: Seven-loop Resummation Results For Ising-like Universality Cmentioning

confidence: 70%

Section: Seven-loop Resummation Results For Ising-like Universality Cmentioning

confidence: 90%

“…[32] and five-loops (ε 5 ) from same reference. The recent results from the non-perturbative renormalization group (NPRG) method [28] For the exponent η, the suitable approximants are:…”

Section: Seven-loop Resummation Results For Ising-like Universality Cmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Critical exponents of the O(N)-symmetric $$\phi ^4$$ model from the $$\varepsilon ^7$$ hypergeometric-Meijer resummation

Shalaby

2021

Eur. Phys. J. C

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Gentle introduction to rigorous Renormalization Group: a worked fermionic example

Giuliani

Mastropietro

Rychkov

2021

J. High Energ. Phys.

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Much of our understanding of critical phenomena is based on the notion of Renormalization Group (RG), but the actual determination of its fixed points is usually based on approximations and truncations, and predictions of physical quantities are often of limited accuracy. The RG fixed points can be however given a fully rigorous and non- perturbative characterization, and this is what is presented here in a model of symplectic fermions with a nonlocal (“long-range”) kinetic term depending on a parameter ε and a quartic interaction. We identify the Banach space of interactions, which the fixed point belongs to, and we determine it via a convergent approximation scheme. The Banach space is not limited to relevant interactions, but it contains all possible irrelevant terms with short-ranged kernels, decaying like a stretched exponential at large distances. As the model shares a number of features in common with ϕ4 or Ising models, the result can be used as a benchmark to test the validity of truncations and approximations in RG studies. The analysis is based on results coming from Constructive RG to which we provide a tutorial and self-contained introduction. In addition, we prove that the fixed point is analytic in ε, a somewhat surprising fact relying on the fermionic nature of the problem.

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Exploring the θ-vacuum structure in the functional renormalization group approach

Fukushima

Shimazaki

Tanizaki

2022

J. High Energ. Phys.

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We investigate the θ-vacuum structure and the ’t Hooft anomaly at θ = π in a simple quantum mechanical system on S1 to scrutinize the applicability of the functional renormalization group (fRG) approach. Even though the fRG is an exact formulation, a naive application of the fRG equation would miss contributions from the θ term due to the differential nature of the formulation. We first review this quantum mechanical system on S1 that is solvable with both the path integral and the canonical quantization. We discuss how to construct the quantum effective action including the θ dependence. Such an explicit calculation poses a subtle question of whether a Legendre transform is well defined or not for general systems with the sign problem. We then consider a deformed theory to relax the integral winding by introducing a wine-bottle potential with the finite depth ∝ g, so that the original S1 theory is recovered in the g → ∞ limit. We numerically solve the energy spectrum in the deformed theory as a function of g and θ in the canonical quantization. We test the efficacy of the simplest local potential approximation (LPA) in the fRG approach and find that the correct behavior of the ground state energy is well reproduced for small θ. When the energy level crossing is approached, the LPA flow breaks down and fails in describing the ground state degeneracy expected from the ’t Hooft anomaly. We finally turn back to the original theory and discuss an alternative formulation using the Villain lattice action. The analysis with the Villain lattice at θ = π indicates that the nonlocality of the effective action is crucial to capture the level crossing behavior of the ground states.

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Precision calculation of critical exponents in the O(N) universality classes with the nonperturbative renormalization group

Cited by 94 publications

References 90 publications

Critical exponents of the O(N)-symmetric $$\phi ^4$$ model from the $$\varepsilon ^7$$ hypergeometric-Meijer resummation

Critical exponents of the O(N)-symmetric $$\phi ^4$$ model from the $$\varepsilon ^7$$ hypergeometric-Meijer resummation

Gentle introduction to rigorous Renormalization Group: a worked fermionic example

Exploring the θ-vacuum structure in the functional renormalization group approach

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