High Energy Physics - Lattice · arXiv:1211.1803 v1 · submitted 8 Nov 2012
Chiral Dynamics With Wilson Fermions
The paper says
“A number of insights on chiral Dynamics with Wilson fermions can be obtained from the computation of the microscopic spectrum of the Wilson Dirac operator.”
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The paper
Abstract
Close to the continuum the lattice spacing affects the smallest eigenvalues of the Wilson Dirac operator in a very specific manner determined by the way in which the discretization breaks chiral symmetry. These effects can be computed analytically by means of Wilson chiral perturbation theory and Wilson random matrix theory. A number of insights on chiral Dynamics with Wilson fermions can be obtained from the computation of the microscopic spectrum of the Wilson Dirac operator. For example, the unusual volume scaling of the smallest eigenvalues observed in lattice simulations has a natural explanation. The dynamics of the eigenvalues of the Wilson Dirac operator also allow us to determine the additional low energy constants of Wilson chiral perturbation theory and to understand why the Sharpe-Singleton scenario is only realized in unquenched simulations.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 0.62
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.24 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| Close to the continuum the lattice spacing affects the smallest eigenvalues of the Wilson Dirac operator in a very specific manner determined by the way in which the discretization breaks chiral symmetry. | background 0.79 | 0.15 | 0.23 | asserted 1.00 |
| These effects can be computed analytically by means of Wilson chiral perturbation theory and Wilson random matrix theory. | method 0.95 | 0.20 | 0.08 | asserted 0.90 |
| A number of insights on chiral Dynamics with Wilson fermions can be obtained from the computation of the microscopic spectrum of the Wilson Dirac operator. | contribution 0.63 | 0.24 | 0.29 | asserted 0.62 |
| For example, the unusual volume scaling of the smallest eigenvalues observed in lattice simulations has a natural explanation. | interpretation 0.61 | 0.22 | 0.12 | asserted 0.99 |
| The dynamics of the eigenvalues of the Wilson Dirac operator also allow us to determine the additional low energy constants of Wilson chiral perturbation theory and to understand why the Sharpe-Singleton scenario is only realized in unquenched simulations. | result 0.65 | 0.56 | 0.31 | asserted 0.99 |
What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.76
What was examined, and what was not
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- arXiv listing abstract v1
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- references and citing sentences
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- T body sentences
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How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,309 input tokens, $0.0002 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
How the literature uses it
5 arXiv papers cite this in 5 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 3 papers
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We refer the reader to [ref] for a review of the recent developments of RMT for the Wilson Dirac operator.
The Effect of the Low Energy Constants on the Spectral Properties of the Wilson Dirac Operator · Introduction · 1.00
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For a recent review with additional references, see Ref. [ref] .
Wilson chiral perturbation theory, Wilson-Dirac operator eigenvalues and clover improvement · Introduction · 1.00
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In Refs. [ref] they have been studied by matching the analytical predictions [ref] for the spectrum of the Wilson Dirac operator – with fixed index in a finite volume – to lattice data.[For a recent review, we refer to [ref] .] Determinations of the Wilson LECs have also been carried out via the spectral density of the Hermitian Wilson-Dirac operator [ref] .
Determination of Low-Energy Constants of Wilson Chiral Perturbation Theory · Introduction · 0.93
What it cites · 50 sentences without a confident label
Uses the method or tool of 1 paper
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One can also evaluate the squared condensate $⟨(iu̅γ_5u+id̅γ_5d)^2⟩$ at zero external sources as suggested in [ref] .
Elucidating the Vacuum Structure of the Aoki Phase · Alternative vacuum in the Aoki phase for $N_f=2$ · 0.90
Uses data or values from 1 paper
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The left hand plot is lattice data obtained in [ref] while the right hand plot gives an example of the analytic results.
Universality of the topological susceptibility in the SU(3) gauge theory · Scaling with $a/√(V)$ · 0.93
Compares with 1 paper
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In [ref] these constants are denoted respectively by $-W_6'$, $-W_7'$ and $-W_8'$.
Chiral perturbation theory at O(a^2) for lattice QCD · Wilson Chiral Perturbation Theory in the $ϵ$-regime · 0.93
Cites as support 3 papers
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Only for W_6<0, W_7<0 and W_8>0 does the Wilson chiral Lagrangian describe lattice QCD with a $γ_5$-Hermitian Wislon Dirac operator [ref] .
Microscopic Spectrum of the Wilson Dirac Operator · Aoki phase and Sharpe-Singleton scenario · 0.97
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Only for W_6<0, W_7<0 and W_8>0 does the Wilson chiral Lagrangian describe lattice QCD with a $γ_5$-Hermitian Wislon Dirac operator [ref] .
Constraint on the Low Energy Constants of Wilson Chiral Perturbation Theory · Aoki phase and Sharpe-Singleton scenario · 0.97
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Only for W_6<0, W_7<0 and W_8>0 does the Wilson chiral Lagrangian describe lattice QCD with a $γ_5$-Hermitian Wislon Dirac operator [ref] .
The Realization of the Sharpe-Singleton Scenario · Aoki phase and Sharpe-Singleton scenario · 0.97
Cites as background 3 papers
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This effect is captured by Wilson chiral perturbation theory [ref] , for which we now give a focused review.
Chiral perturbation theory for the Wilson lattice action · Wilson Chiral Perturbation Theory in the $ϵ$-regime · 0.85
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This effect is captured by Wilson chiral perturbation theory [ref] , for which we now give a focused review.
Chiral perturbation theory at O(a^2) for lattice QCD · Wilson Chiral Perturbation Theory in the $ϵ$-regime · 0.85
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We refer to [ref] for details.
New Ways to Determine Low-Energy Constants with Wilson Fermions · Spectrum of the Hermitian Wilson Dirac operator · 0.88
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