Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:01:57.021870Z
Paper Citation Record · LEDGER
As of 7 August 2026, this Paper Citation Record lists 90 of 90 outbound references and 1 inbound Pith citation observation for arXiv:2506.09142.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:01:57.021870Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-06T12:11:01.153016Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-06T12:11:01.266822Z
90 of 90 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation c013a11b-ba8f-4999-94a4-ce97da6eda13 · outbound
Critical scaling for spectral functions (15) Owing to Lorentz invariance, the propagator is fully de- termined by its values at vanishing spatial momentum
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d010e0f4-91d3-4e61-bed1-124e8482eb5f · outbound
Critical scaling for spectral functions We follow [1, 3, 6, 11] and use the inhomogeneous Bethe- Salpeter equation with a classical scattering kernel
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f0e103bc-a7ff-41fc-ae96-f3d901f7e33b · outbound
Critical scaling for spectral functions The momentum-independent part is cancelled by the counter term S(2) ct in (12) due to the renormalisation condition (11)
Reference 3
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8edd5781-b107-4ae6-9fb9-632670828162 · outbound
Critical scaling for spectral functions Quark propagator in Minkowski space
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 134e33d9-ea99-4dc2-94b9-33d486a712e7 · outbound
Critical scaling for spectral functions Our numerical results for the spectral functions are shown in the doubly logarithmic plots in Figure 2
Reference 5
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a214568c-e2a4-47fa-89c6-4eff3420428b · outbound
Critical scaling for spectral functions The third method consists of using the k- scaling of the wave function at the pole as a proxy for the momentum and spectral scaling
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9f32b90b-3980-44e2-b668-48deb9848c86 · outbound
Critical scaling for spectral functions To extract the limit k → 0 we per- form an extrapolation
Reference 7
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9e6be460-8cb6-44c3-b1cd-3ac4b3e98e78 · outbound
Critical scaling for spectral functions Thus, to get a value for the (constant) anomalous dimension, we now have to take the limit λ → 0
Reference 8
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3722f3b5-f099-4460-8902-222be278f065 · outbound
Critical scaling for spectral functions The two-point function (and therefore the spectral function) was calculated on a logarithmic momentum grid, which over the course of the flow was expanded to include lower momenta
Reference 9
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a4902efa-0ab9-4f77-95e1-7642dc4df60c · outbound
Critical scaling for spectral functions Unresolved cited work
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1b054c7d-9a8f-4476-a325-f8d81f8210cc · outbound
Critical scaling for spectral functions In the deep IR, the finite numerical precision leads to small, numeri- cal deviations from the sum rule, which, if not corrected, can build up to destabilize the flow
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation adee22e4-5ce2-4424-93c8-fd4645523344 · outbound
Critical scaling for spectral functions Unresolved cited work
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 32bed362-61d5-4c5b-a8e8-2e498408ec72 · outbound
Critical scaling for spectral functions Unresolved cited work
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 5ee7aaa3-f8bc-4a4f-b78f-b8c5c328e02b · outbound
Critical scaling for spectral functions This can be accommo- dated for by coupling the flow of the propagator to that of the effective potential
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation a8b75591-6770-429d-ada3-458d17ca7319 · outbound
Critical scaling for spectral functions In scalar models, momentum dependences can be incorporated with the BMW-approximation [53– 55], for applications see [15]
Reference 15
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Unavailable: canonical work link unavailable.
Observation dca53ba8-8bca-4602-adfe-d6647b13401e · outbound
Critical scaling for spectral functions Here, p is the external mo- mentum and q the loop momentum
Reference 16
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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 127bbe29-9b1b-4781-9219-d6968c32db8d · outbound
Critical scaling for spectral functions Renormalised spectral flows
Reference 17
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Unavailable: canonical work link unavailable.
Observation ecf72871-36cd-4c21-ad7c-85f2fef7e019 · outbound
Critical scaling for spectral functions Lorentzian quantum gravity and the graviton spectral function
Reference 18
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Unavailable: canonical work link unavailable.
Observation bbefed51-e151-49cb-a630-a816026f3b61 · outbound
Critical scaling for spectral functions Scalar spectral functions from the spectral fRG
Reference 19
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Unavailable: canonical work link unavailable.
Observation e3eb89ba-ca29-4109-b054-88bbba4c8543 · outbound
Critical scaling for spectral functions Fermion and Photon gap-equations in Minkowski space within the Nakanishi Integral Representation method
Reference 20
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0b445701-55f3-4cd7-ae52-b2a91bf6736b · outbound
Critical scaling for spectral functions Spectral functions in the $\phi^4$-theory from the spectral DSE
Reference 21
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Unavailable: canonical work link unavailable.
Observation db902bf0-a5cd-4d91-8feb-d1786ce0b2e9 · outbound
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 6c1f1de1-e119-4e61-9efb-b17dd5304bb4 · outbound
Critical scaling for spectral functions On the complex structure of Yang-Mills theory
Reference 23
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Unavailable: canonical work link unavailable.
Observation 0292ce49-66d5-4b2b-8c66-73f720cee176 · outbound
Critical scaling for spectral functions On the quark spectral function in QCD
Reference 24
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Unavailable: canonical work link unavailable.
Observation 1d18b4cf-5134-457e-94b0-658156e1b210 · outbound
Critical scaling for spectral functions The causal structure of the quark propagator
Reference 25
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Unavailable: canonical work link unavailable.
Observation b1b151f6-b4b4-4830-ac52-b1c995997f50 · outbound
Critical scaling for spectral functions Bound states from the spectral Bethe-Salpeter equation
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e8fc8797-373d-4c44-a35d-d66861735a0d · outbound
Critical scaling for spectral functions Ising exponents from the functional renormalisation group
Reference 27
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Unavailable: canonical work link unavailable.
Observation 3650e304-1ebd-482e-865d-8ca6eb87a4b8 · outbound
Critical scaling for spectral functions Convergence of Non-Perturbative Approximations to the Renormalization Group
Reference 28
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Unavailable: canonical work link unavailable.
Observation 392c1d2e-e997-4a0a-af71-9ba136e67365 · outbound
Critical scaling for spectral functions Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
Reference 29
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Unavailable: canonical work link unavailable.
Observation 1555ff70-c93b-4d54-8b68-c935fd4a1c97 · outbound
Critical scaling for spectral functions The nonperturbative functional renormalization group and its applications
Reference 30
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Unavailable: canonical work link unavailable.
Observation 9b8afd47-38e2-47bc-845a-88e602e137f5 · outbound
Critical scaling for spectral functions Solving the 3D Ising Model with the Conformal Bootstrap
Reference 31
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Observation d8906a0f-9857-490f-828f-eb257d74d555 · outbound
Critical scaling for spectral functions Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
Reference 32
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Unavailable: canonical work link unavailable.
Observation 865d0b9e-e973-4842-97cb-1a28cb545d54 · outbound
Critical scaling for spectral functions Functional renormalisation group approach to far-from-equilibrium quantum field dynamics
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 902747d3-a967-4d7d-bcff-6b21f86422fd · outbound
Critical scaling for spectral functions Nonthermal fixed points and the functional renormalization group
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ce42e980-92ba-4917-8610-18c66efe591e · outbound
Critical scaling for spectral functions Far-from-equilibrium quantum many-body dynamics
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 76ad3b6d-e0e8-4eb5-a420-92b5659fced4 · outbound
Critical scaling for spectral functions Analytic continuation of functional renormalization group equations
Reference 36
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Unavailable: canonical work link unavailable.
Observation b3b56d32-c6ab-469e-b1df-e8076f004365 · outbound
Critical scaling for spectral functions Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group
Reference 37
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Unavailable: canonical work link unavailable.
Observation 054a4955-fe7d-421e-9098-ce2cdc62e567 · outbound
Critical scaling for spectral functions Dynamic universality class of Model C from the functional renormalization group
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 3a3902e6-8789-4072-b2fb-b41f991016de · outbound
Critical scaling for spectral functions Spectral Functions for the Quark-Meson Model Phase Diagram from the Functional Renormalization Group
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a1e4de48-78df-4192-b91c-9e8a8a9fe316 · outbound
Critical scaling for spectral functions Real time correlation functions and the functional renormalisation group
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 995f73d2-3c87-46a9-b666-73f7c6427546 · outbound
Critical scaling for spectral functions Mobile impurity in a Fermi sea from the functional renormalization group analytically continued to real time
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 42145c5a-65a6-4fc8-b847-a112510dfa4c · outbound
Critical scaling for spectral functions In-Medium Spectral Functions of Vector- and Axial-Vector Mesons from the Functional Renormalization Group
Reference 42
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Unavailable: canonical work link unavailable.
Observation d3b86f35-b959-4947-9aee-6109287e49ee · outbound
Critical scaling for spectral functions Finite temperature spectral functions in the O(N)-model
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 56b45ad4-f102-4646-9679-61867a449521 · outbound
Critical scaling for spectral functions Meson Spectral Functions at Finite Temperature and Isospin Density with Functional Renormalization Group
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 87d819ec-571b-4d32-a268-f1aca405d072 · outbound
Critical scaling for spectral functions In-medium spectral functions and dilepton rates with the Functional Renormalization Group
Reference 45
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Unavailable: canonical work link unavailable.
Observation 1299aa53-a606-4e02-afb8-85f087be9c6e · outbound
Critical scaling for spectral functions Fermionic spectral functions with the Functional Renormalization Group
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ca56b27f-4130-4ac1-8e26-e4d4fe1b2f48 · outbound
Critical scaling for spectral functions Flowing with the Temporal Renormalisation Group
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 47eb467f-61ea-49c8-a7df-631ffabf2d1c · outbound
Critical scaling for spectral functions Spectral functions from the real-time functional renormalization group
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b1296002-1a80-4a9c-8ef0-7e4abe47d02b · outbound
Critical scaling for spectral functions Self-consistent $O(4)$ model spectral functions from analytically continued FRG flows
Reference 49
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2dc658a4-f093-4b4e-8e1a-ee5749648856 · outbound
Critical scaling for spectral functions Real-time dynamics of the $O(4)$ scalar theory within the fRG approach
Reference 50
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4a735f2c-f04d-4bfe-b31c-a14c7bf855a9 · outbound
Critical scaling for spectral functions Causal Temporal Renormalisation Group Flow of the Energy-Momentum Tensor
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 8f8bd733-f17b-417a-aef2-eeffaccb61fc · outbound
Critical scaling for spectral functions Real-time methods for spectral functions
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 70a472d2-398a-4c66-bbc8-e9717ef01f21 · outbound
Critical scaling for spectral functions Critical dynamics in a real-time formulation of the functional renormalization group
Reference 53
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Unavailable: canonical work link unavailable.
Observation 7c5b8314-f056-42f4-baf2-dd3cff12a6e7 · outbound
Critical scaling for spectral functions Dynamic critical behavior of the chiral phase transition from the real-time functional renormalization group
Reference 54
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Unavailable: canonical work link unavailable.
Observation 9e26a3b6-119d-4c86-bc97-cb979a8a7172 · outbound
Critical scaling for spectral functions Universal critical dynamics near the chiral phase transition and the QCD critical point
Reference 55
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 64451e81-0c6b-44c9-8649-6440c003fd9e · outbound
Critical scaling for spectral functions Phase structure of quark matter and in-medium properties of mesons from Callan-Symanzik flows
Reference 56
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cdadbab8-1581-40fc-98e2-96392344f762 · outbound
Critical scaling for spectral functions The QCD moat regime and its real-time properties
Reference 57
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Unavailable: canonical work link unavailable.
Observation 180149d9-7135-4487-a46c-459ace34b79c · outbound
Critical scaling for spectral functions Effects of dissipation on phase diagram and bosonic excitations in the quark-meson model
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 02cfda05-94e1-4c9d-be16-294ba875f6aa · outbound
Critical scaling for spectral functions Flow Equations for the Relevant Part of the Pure Yang-Mills Action
Reference 59
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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 645f4406-03cf-4318-a143-677e106e18e5 · outbound
Critical scaling for spectral functions The Heavy Quark Potential from Wilson's Exact Renormalization Group
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0117fbc2-f5e2-472c-9c17-dfc4e84a2818 · outbound
Critical scaling for spectral functions Effective Quark Interactions and QCD-Propagators
Reference 61
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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 2265ee6e-98fe-4469-899b-747a8ead6d7d · outbound
Critical scaling for spectral functions Unresolved cited work
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e2c4df32-4542-4608-8913-379f86949c63 · outbound
Critical scaling for spectral functions Chiral symmetry breaking in continuum QCD
Reference 63
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Unavailable: canonical work link unavailable.
Observation 18fea37b-1caa-4758-8a1e-b0792baa706b · outbound
Critical scaling for spectral functions Non-perturbative quark, gluon and meson correlators of unquenched QCD
Reference 64
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Unavailable: canonical work link unavailable.
Observation 6eb309ec-1fa5-4130-9112-99ad7e834526 · outbound
Critical scaling for spectral functions Towards quantitative precision in functional QCD I
Reference 65
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Observation 0e0013ef-50d9-43b9-b11d-b68afafbe813 · outbound
Critical scaling for spectral functions Four-quark scatterings in QCD III
Reference 66
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Observation 7f6162d5-efff-4aa0-813e-f1d9f26600bb · outbound
Critical scaling for spectral functions github.io/
Reference 67
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Observation a9cfaa6d-4299-42c7-a515-ad1dfaf3549d · outbound
Critical scaling for spectral functions A new method to solve the Non Perturbative Renormalization Group equations
Reference 68
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Observation 56620169-3ca2-4d97-b724-6aeb75cf25dc · outbound
Critical scaling for spectral functions Non perturbative renormalisation group and momentum dependence of $n$-point functions (I)
Reference 69
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Observation 767d01f3-a500-4690-9c84-6998ee6e106f · outbound
Critical scaling for spectral functions Non perturbative renormalization group and momentum dependence of n-point functions (II)
Reference 70
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Observation a69551a5-ef60-4a9e-bf97-192aa366e375 · outbound
Critical scaling for spectral functions Towards quantitative precision in the chiral crossover: masses and fluctuation scales
Reference 71
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Observation b4657e1b-9818-4ee6-822b-41c126226c1a · outbound
Critical scaling for spectral functions Reconstructing the gluon
Reference 72
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Observation c9945395-e9bb-4040-94ac-6d09e6198258 · outbound
Critical scaling for spectral functions Reconstructing the graviton
Reference 73
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Unavailable: canonical work link unavailable.
Observation 5847c440-14da-4913-a756-1b85fae96188 · outbound
Critical scaling for spectral functions Fully coupled functional equations for the quark sector of QCD
Reference 74
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Observation f8e5d7fa-5b1c-4d5d-a68b-e2e2a42c500d · outbound
Critical scaling for spectral functions Unresolved cited work
Reference 75
Source-reported events for the cited work
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Observation a795b79f-4a36-40b8-a716-b303ff0c732d · outbound
Critical scaling for spectral functions Unresolved cited work
Reference 76
Source-reported events for the cited work
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Observation 9c27021c-f264-4ed6-a534-c220bd1bcb89 · outbound
Critical scaling for spectral functions Critical exponents from optimised renormalisation group flows
Reference 77
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Observation 2288bb16-4258-4dd6-984f-c2339c57982b · outbound
Critical scaling for spectral functions Aspects of the Functional Renormalisation Group
Reference 78
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Observation c15fcb84-4aab-4e8f-aa4d-97c4af16adad · outbound
Critical scaling for spectral functions Physics and the choice of regulators in functional renormalisation group flows
Reference 79
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Observation 4c9a6e4c-59e4-4868-bf94-4da5bec637f7 · outbound
Critical scaling for spectral functions Flowing fields and optimal RG-flows
Reference 80
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Observation 03e4d71a-90c5-4979-9391-1e2c341639a2 · outbound
Critical scaling for spectral functions Physics-informed renormalisation group flows
Reference 81
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Observation f92d0b08-644b-457e-9b2f-034af70925b7 · outbound
Critical scaling for spectral functions Bezanson, A
Reference 82
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Observation 28885092-973f-48fd-bda4-d69c73540c5b · outbound
Critical scaling for spectral functions Resolving phase transitions with Discontinuous Galerkin methods
Reference 83
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Observation 710bef10-ebce-4e8b-b3e7-4892cd16ae4a · outbound
Critical scaling for spectral functions Shocks and quark-meson scatterings at large density
Reference 84
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Unavailable: canonical work link unavailable.
Observation f7e68ac8-53b3-4708-a367-e3bc644e4de1 · outbound
Critical scaling for spectral functions Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model
Reference 85
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Unavailable: canonical work link unavailable.
Observation 78e76031-eeb3-4325-b5d3-1ed9b5142390 · outbound
Critical scaling for spectral functions Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows
Reference 86
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1942f9ba-dce8-46d2-914b-dc03ab30eca3 · outbound
Critical scaling for spectral functions Local Discontinuous Galerkin for the Functional Renormalisation Group
Reference 87
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Unavailable: canonical work link unavailable.
Observation 6ce121eb-ecca-480b-b8bb-d0db26a7ace9 · outbound
Critical scaling for spectral functions Numerical RG-time integration of the effective potential: Analysis and Benchmark
Reference 88
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Observation 90e7704d-e8d8-4b31-95c2-e186547bdfb0 · outbound
Critical scaling for spectral functions Towards quantitative precision for QCD at large densities
Reference 89
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Unavailable: canonical work link unavailable.
Observation a63d37a6-5a3d-43ee-8532-4f49a2f123ef · outbound
Critical scaling for spectral functions Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space
Reference 90
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Observation 0ee62a34-4b7e-4a64-8821-061dd19bd005 · inbound
Self-consistent graviton spectral function in Lorentzian quantum gravity Critical scaling for spectral functions
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.