Precision calculation of universal amplitude ratios in O(
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) universality classes: Derivative expansion results at order 
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Polsi, Gonzalo De; Hernández-Chifflet, Guzmán; Wschebor, Nicolás

doi:10.1103/physreve.104.064101

Cited by 19 publications

(12 citation statements)

References 96 publications

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“…We limit the discussion to methods used to find perturbative data in the various expansion limits, and therefore omit methods such as the numerical conformal bootstrap [38], Monte Carlo simulations (e.g. [151,152]), high temperature expansions [15], non-perturbative/functional RG methods [64,143,183,[223][224][225][226] and fixed-dimension expansions [227][228][229].…”

Section: Methodsmentioning

confidence: 99%

“…An important class of observables, directly measurable in experiments and Monte Carlo simulations, are universal amplitude ratios [182]. Since they are not defined in terms of conformal data, they generally fall outside the scope of this report, and for a complete treatment we refer to the [25] and to the more recent paper [183] from the point of view of the non-perturbative RG.…”

Section: Universal Amplitude Ratiosmentioning

confidence: 99%

“…For more detailed tables of values of U 0 computed using different methods. see [155,188] for N = 1 and [183] for N = 2, 3, 4, 5. For N = 1, an experiment on succinonitrile-water mixture gave U 0 = 0.536(5) [189].…”

Section: Universal Amplitude Ratiosmentioning

confidence: 99%

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The critical O(N) CFT: Methods and conformal data

Henriksson¹

2022

Preprint

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The critical O(N ) CFT in spacetime dimensions 2 < d < 4 is one of the most important examples of a conformal field theory, with the Ising CFT at N = 1, 2 d < 4, as a notable special case. Apart from numerous physical applications, it serves frequently as a concrete testing ground for new approaches and techniques based on conformal symmetry. In the perturbative limits -the 4 − ε expansion, the large N expansion and the 2 + ˜ expansion -a lot of conformal data have been computed over the years. In this report, we give an overview of the critical O(N ) CFT, including some methods to study it, and present a large collection of conformal data. The data, extracted from the literature and supplemented by many additional computations of order ε anomalous dimensions, is made available through an ancillary data file..

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Section: Methodsmentioning

confidence: 99%

Section: Universal Amplitude Ratiosmentioning

confidence: 99%

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The critical O(N) CFT: Methods and conformal data

Henriksson¹

2022

Preprint

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“…For a detailed description, we refer the reader to Ref. [69,70]. The fixed point solution (for real values of ρ0 ) describes the Wilson-Fisher fixed point.…”

Section: Wilson-fischer Fixed Point Solutionmentioning

confidence: 99%

Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d \le 4$

Rennecke,

Skokov

2022

Preprint

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“…Therefore, the fRG equation, particularly the Wetterich equation that we employ in this work, makes interpolation between the known UV action, Γ Λ = S, and the IR effective action, Γ 0 = Γ. We should emphasize that the fRG equation by itself is exact without any approximation, and one can thus define the theory nonperturbatively with the fRG equation and the initial condition; Γ Λ = S. There are a countless number of successful fRG applications such as the O(N ) models [18][19][20][21][22][23], the Quark-Meson model [24][25][26][27][28][29][30][31][32][33], the Nambu-Jona-Lasinio mode [34], quantum chromodynamics (QCD) [35][36][37][38], the quantum gravity [39][40][41][42], etc. It is simply impossible to mention all the progresses here, and the fRG prospects are further expanding.…”

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confidence: 99%

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

Fukushima,

Shimazaki,

Tanizaki

2022

Preprint

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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 S 1 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 S 1 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 S 1 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 universal amplitude ratios in O( N ) universality classes: Derivative expansion results at order O(∂4)

Cited by 19 publications

References 96 publications

The critical O(N) CFT: Methods and conformal data

The critical O(N) CFT: Methods and conformal data

Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d \le 4$

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

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