Conformal invariance in the nonperturbative renormalization group: A rationale for choosing the regulator

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

doi:10.1103/physreve.101.062146

Cited by 22 publications

(15 citation statements)

References 32 publications

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“…We attribute the inaccuracies concerning the numerical values of the exponents to the low level of the implemented truncation and point out that the case of d = 2 is the least favorable for the present approach due to relatively large values of the anomalous dimension. [19,20,22,23] The accuracy of our method is expected to increase upon raising d. It is nonetheless doubtless from our above results that the second-order DE is able to capture nonanalytic behavior of the critical exponents at (d, N ) = (2, 2). In the following section we use an analogous strategy in an attempt to identify the nonanalyticities at d > 2 expected to occur along the C-H line.…”

Section: Dimensionality D =mentioning

confidence: 84%

“…For the less complex case of Ising symmetry-breaking (N = 1) the computation was performed [20] even up to order ∂ 6 . In addition to numbers (including errorbars), these studies delivered insights pointing towards rapid convergence of the DE, emphasizing (and clarifying [23]) the role of the so-called principle of minimal sensitivity (PMS) [24]. The latter amounts to demanding that the analyzed quantity (e.g.…”

Section: Functional Rg and The Derivative Expansionmentioning

confidence: 99%

“…with a variable parameter α. Refs. [22,23] reveal the increasing role of the PMS principle in high-precision evaluation of the critical indices upon elevating the truncation order. At the ∂ 2 order of the DE this dependence is however relatively modest.…”

Section: Regulator Choicementioning

confidence: 99%

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Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Chlebicki

Jakubczyk

2021

SciPost Phys.

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We employ the functional renormalization group framework at the second order in the derivative expansion to study the O(N)O(N) models continuously varying the number of field components NN and the spatial dimensionality dd. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents \nuν and \etaη across a line in the (d,N)(d,N) plane, which passes through the point (2,2)(2,2). By direct numerical evaluation of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as well as analysis of the functional fixed-point profiles, we find clear indications of this line in the form of a crossover between two regimes in the (d,N)(d,N) plane, however no evidence of discontinuous or singular first and second derivatives of these functions for d>2d>2. The computed derivatives of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) become increasingly large for d\to 2d→2 and N\to 2N→2 and it is only in this limit that \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as obtained by us are evidently nonanalytical. By scanning the dependence of the subleading eigenvalue of the RG transformation on NN for d>2d>2 we find no indication of its vanishing as anticipated by the Cardy-Hamber scenario. For dimensionality dd approaching 3 there are no signatures of the Cardy-Hamber line even as a crossover and its existence in the form of a nonanalyticity of the anticipated form is excluded.

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Section: Dimensionality D =mentioning

confidence: 84%

Section: Functional Rg and The Derivative Expansionmentioning

confidence: 99%

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Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Chlebicki

Jakubczyk

2021

SciPost Phys.

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“…As a side note, we point out a recent proposal for an alternative way to fix the regulator dependence for conformally invariant theories, the principle of maximal conformality (PMC) [71]. Conformal invariance implies a set of (modified) Ward identities associated with scale and special conformal transformations (SCT).…”

Section: Numerical Resultsmentioning

confidence: 99%

Operator product expansion coefficients from the nonperturbative functional renormalization group

Rose,

Pagani,

Dupuis

2021

Preprint

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Using the nonperturbative functional renormalization group (FRG) within the Blaizot-Méndez-Galain-Wschebor approximation, we compute the operator product expansion (OPE) coefficient c112 associated with the operators O1 ∼ ϕ and O2 ∼ ϕ 2 in the three-dimensional O(N ) universality class and in the Ising universality class (N = 1) in dimensions 2 ≤ d ≤ 4. When available, exact results and estimates from the conformal bootstrap and Monte-Carlo simulations compare extremely well to our results, while FRG is able to provide values across the whole range of d and N considered.

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“…The obtained value of ν −1 ⊥ carries a weak dependence on α. In accord with the principle of minimal sensitivity 72,73 (PMS) one chooses α so that ν −1 ⊥ is locally stationary with respect to variation of α. Our results for ν ⊥ depending on N, d and m are presented in Figs.…”

Section: B Local Potential Approximationmentioning

confidence: 99%

Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points

Zdybel,

Homenda,

Chlebicki

et al. 2021

Preprint

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We revisit the question concerning stability of nonuniform superfluid states of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type to thermal and quantum fluctuations. Invoking the properties of the putative phase diagram of two-component Fermi mixtures, on general grounds we argue, that for isotropic, continuum systems the phase diagram hosting a long-range-ordered FFLO-type phase envisaged by the mean-field theory cannot be stable to fluctuations at any temperature T > 0 in any dimensionality d < 4. In contrast, in layered unidirectional systems the lower critical dimension for the onset of FFLO-type long-range order accompanied by a Lifshitz point at T > 0 is d = 5/2. In consequence, its occurrence is excluded in d = 2, but not in d = 3. We propose a relatively simple method, based on nonperturbative renormalization group to compute the critical exponents of the thermal m-axial Lifshitz point continuously varying m, spatial dimensionality d and the number of order parameter components N. We point out the possibility of a robust, fine-tuning free occurrence of a quantum Lifshitz point in the phase diagram of imbalanced Fermi mixtures.

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Conformal invariance in the nonperturbative renormalization group: A rationale for choosing the regulator

Cited by 22 publications

References 32 publications

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

Operator product expansion coefficients from the nonperturbative functional renormalization group

Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points

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