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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Cosmological constraints from the cross-correlation of DESI Luminous Red Galaxies with CMB lensing from Planck PR4 and ACT DR6

Here, we infer the growth of large scale structure over the redshift range 0.4 ≲ z ≲ 1 from the cross-correlation of spectroscopically calibrated Luminous Red Galaxies (LRGs) selected from the Dark Energy Spectroscopic Instrument (DESI) legacy imaging survey with CMB lensing maps reconstructed from the latest Planck and ACT data. We adopt a hybrid effective field theory (HEFT) model that robustly regulates the cosmological information obtainable from smaller scales, such that our cosmological constraints are reliably derived from the (predominantly) linear regime. We perform an extensive set of bandpower- and parameter-level systematics checks to ensure the robustness of our results and to characterize the uniformity of the LRG sample. We demonstrate that our results are stable to a wide range of modeling assumptions, finding excellent agreement with a linear theory analysis performed on a restricted range of scales. From a tomographic analysis of the four LRG photometric redshift bins we find that the rate of structure growth is consistent with ΛCDM with an overall amplitude that is ≃ 5-7% lower than predicted by primary CMB measurements with modest (∼ 2σ) statistical significance. From the combined analysis of all four bins and their cross-correlations with Planck we obtain S 8 = 0.765 ± 0.023, which is less discrepant with primary CMB measurements than previous DESI LRG cross Planck CMB lensing results. From the cross-correlation with ACT we obtain S 8 = 0.790 +0.024 -0.027 , while when jointly analyzing Planck and ACT we find S 8 = 0.775 +0.019 -0.022 from our data alone and σ 8 = 0.772 +0.020 -0.023 with the addition of BAO data. These constraints are consistent with the latest Planck primary CMB analyses at the ≃ 1.6-2.2σ level, and are in excellent agreement with galaxy lensing surveys.

cosmological parameters from LSS↗
DOE OSTI2025

Window convolution of the galaxy clustering bispectrum

In galaxy survey analysis, the observed clustering statistics do not directly match theoretical predictions but rather have been processed by a window function that arises from the survey geometry including the sky footprint, redshift-dependent background number density and systematic weights. While window convolution of the power spectrum is well studied, for the bispectrum with a larger number of degrees of freedom, it poses a significant numerical and computational challenge. In this work, we consider the effect of the survey window in the tripolar spherical harmonic decomposition of the bispectrum and lay down a formal procedure for their convolution via a series expansion of configuration-space three-point correlation functions, which was first proposed by Sugiyama et al. (2019). We then provide a linear algebra formulation of the full window convolution, where an unwindowed bispectrum model vector can be directly premultiplied by a window matrix specific to each survey geometry. To validate the pipeline, we focus on the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) luminous red galaxy (LRG) sample in the South Galactic Cap (SGC) in the redshift bin 0.4 ≤ z ≤ 0.6. We first perform convergence checks on the measurement of the window function from discrete random catalogues, and then investigate the convergence of the window convolution series expansion truncated at a finite of number of terms as well as the performance of the window matrix. This work highlights the differences in window convolution between the power spectrum and bispectrum, and provides a streamlined pipeline for the latter for current surveys such as DESI and the Euclid mission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Analysis of the inter-species power balance in JET plasmas

Most auxiliary heating methods provide heating to more than one particle species (electrons, ions, impurities) in a fusion plasma. This can lead to substantial temperature differences between species, depending on conditions such as heating power to the different species and collisionality, with temperature differences between species limited by inter-species thermal equipartition and transport. The analysis of the steady-state electron-ion and impurity-ion power balances presented in this paper are used for consistency-checking experimental ion and electron temperature measurements and for inferring the main ion temperature from measured impurity temperatures. As ion temperature measurements by charge exchange spectroscopy (CXS) based on impurity ions have become more difficult and time-consuming since the installation of the ITER-like wall (ILW) with Be and W PFC's, knowing the maximum sustainable temperature difference between ions and electrons, |T i -T e | allows rejecting erroneous measurements. It also obviates the need for an ion temperature measurement, if an electron temperature measurement is available and |T i - T e | cannot be larger than the combined errors of the underlying measurements. A power balance analysis is also required for estimating the errors of the ion and electron heat fluxes prior to any species-resolved transport analysis. The ion-impurity temperature differences are usually found to be small due to strong thermal equipartition between ion species. However, they can approach 10% in JET-ILW low density, high power discharges, such the ones under development for a future JET deuterium–tritium campaign (Joffrin et al 2019 Nucl. Fusion). This has a generally small, but not always negligible effect on the calculation of fusion reaction rates, which depend on main ion temperatures. An important outcome of this analysis is that temperature differences between impurity species are always much smaller than between the impurities and hydrogenic species and can usually be neglected. The article presents two methods for calculating the impurity-to-main ion temperature ratio. Finally, this analysis leads to a method for the reconstruction ion temperature profiles from ion temperature data available at only one or a small number of spatial locations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Cause and impact of low-frequency chirping modes in DIII-D hybrid discharges

Significant variations in MHD activity and fast-ion transport are observed in the DIIID high-beta, steady-state hybrid discharges with a mixture of Electron Cyclotron (EC) waves and Neutral Beam Injection (NBI). When Electron Cyclotron Heating (ECH) or Current Drive (ECCD) is applied, Alfven Eigenmodes (AEs) are usually suppressed and replaced by low-frequency bursting modes. The analysis of a recently compiled database of hybrid discharges suggests that the change of the fast-ion pressure especially the perpendicular pressure is the main factor responsible for the instability transition. The lower ratio of fast-ion injection speed v inj to Alfven speed v alfven and slight drop of safety factor q min during ECCD may also facilitate the transition. The database shows that AEs mainly occur when the fast-ion fraction P f /P total is less than 0.53 and v inj /v alfven is greater than 0.50, while low-frequency bursting modes appear in the opposite regime. In this research, P f and P total are the central fast-ion pressure from classical prediction and total plasma pressure, respectively. The reason why the instability transition correlates with P f /P total and v inj /v alfven is that they can significantly modify the drive of low-frequency bursting modes and AEs. The explanation is supported by the observation that low-frequency bursting modes are rarely seen in the hybrids with NBI only, with EC waves and counter-NBI, or with high plasma density. A careful check of the low-frequency bursting modes suggests that they are mainly chirping (neoclassical) tearing modes [referred to as chirping (N)TM], i.e. the mode frequency firstly jumps up from the steady (N)TM frequency, then chirps down, and finally returns to the steady (N)TM frequency. Sometimes, the (N)TMs are fully stabilized and replaced with pure fishbones. Lastly, the resonance condition calculation and ’Kick’ model simulations suggest that (N)TMs and fishbones can interact through modification of the fast ion distribution in phase space, which influences the drive.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

The status of the Japanese material properties handbook and the challenge to facilitate structural design criteria for DEMO in-vessel components

This work summarizes the current status of the material properties handbook for a structural design using Japanese reduced-activation ferritic/martensitic steel F82H. Specifically, the key structural parameters, e.g. time-independent/dependent design stresses and fatigue design curves, were determined by following the French structural design code RCC-MRx. Moreover, under the Japan–U.S. collaboration, tensile data were newly added to the benchmark heavy irradiation data up to 80 dpa, as critical input information in the intermediate check and review in Japan. Furthermore, the status of structural material data and the near-term and long-term issues were clarified by the evaluation using the attribute guides. In parallel, the structural design approaches, which were newly introduced and extended to cope with the structural design issues under the complex environmental conditions peculiar to the DEMO reactor, were noted with the initial R&D results. Of the many design issues, the multi-axial loading conditions due to the complexity of the DEMO reactor as well as the coolant compatibility and the irradiation effect are mentioned. For example, in the paper, multi-axial fatigue–creep testing and evaluation using the modified universal slope method and brittle/ductile fracture testing and evaluation using the local approach are explained toward DEMO.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

3D radiated power analysis of JET SPI discharges using the Emis3D forward modeling tool

Abstract Precise values for radiated energy in tokamak disruption experiments are needed to validate disruption mitigation techniques for burning plasma tokamaks like ITER and SPARC. Control room analysis of radiated power ( P rad ) on JET assumes axisymmetry, since fitting 3D radiation structures with limited bolometry coverage is an under-determined problem. In mitigated disruptions, radiation is toroidally asymmetric and 3D, due to fast-growing 3D MHD modes and localized impurity sources. To address this problem, Emis3D adopts a physics motivated forward modeling (‘guess and check’) approach, comparing experimental bolometry data to synthetic data from user-defined radiation structures. Synthetic structures are observed with the Cherab modeling framework and a best fit chosen using a reduced χ 2 statistic. 2D tomographic inversion models are tested, as well as helical flux tubes and 3D MHD simulated structures from JOREK. Two nominally identical pure neon shattered pellet injection (SPI) mitigated discharges in JET are analyzed. 2D tomographic inversions with added toroidal freedom are the best fits in the thermal quench (TQ) and current quench (CQ). In the pre-TQ, 2D reconstructions are statistically the best fits, but are likely over-optimized and do not capture the 3D radiation structure seen in fast camera images. The next-best pre-TQ fits are helical structures that extend towards the high-field side, consistent with an impurity flow under the magnetic nozzle effect also observed in JOREK simulations. Whole-disruption radiated fractions of 0.98 + 0.03 / − 0.29 and 1.01 + 0.02 / − 0.17 are found, suggesting that the stored energy may have been fully mitigated by each SPI, although mitigation efficiencies well below ITER and SPARC requirements for high energy pulses are still within the large uncertainties. Emis3D is also used to validate JOREK SPI simulations, and confirms improvements in matching experiment from changes to impurity modeling. Time-dependent toroidal peaking factors are calculated and discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Dynamical chemistry: non-equilibrium effective actions for reactive fluids

Abstract We present two approaches for describing chemical reactions taking place in fluid phase. The first method mirrors the usual derivation of the hydrodynamic equations of motion by relating conserved—or to account for chemical reactions, non-conserved—currents to local-equilibrium parameters. The second method involves a higher-brow approach in which we attack the same problem from the perspective of non-equilibrium effective field theory (EFT). Non-equilibrium effective actions are defined using the in–in formalism on the Schwinger–Keldysh contour and are therefore capable of describing thermal fluctuations and dissipation as well as quantum effects. The non-equilibrium EFT approach is especially powerful as all terms in the action are fully specified by the symmetries of the system; in particular the second law of thermodynamics does not need to be included by hand, but is instead derived from the action itself. We find that the equations of motion generated by both methods agree, but the EFT approach yields certain advantages. To demonstrate some of these advantages we construct a quadratic action that is valid to very small distance scales—much smaller than the scales at which ordinary hydrodynamic theories break down. Such an action captures the full thermodynamic and quantum behavior of reactions and diffusion at quadratic order. Finally, taking the low-frequency and low-wavenumber limit, we reproduce the linearized version of the well-known reaction–diffusion equations as a final coherence check.

Mechanics↗
DOE OSTI2024

Robust wind farm layout optimization

Wake interactions in wind farms cause losses in annual energy production (AEP) on the order of 10%. Wind farm designers optimize the layout of the farm to mitigate wake losses, especially in the dominant site-specific wind directions. As wind turbines and wind farms grow in scale, optimization becomes more complex. Offshore wind farms regularly comprise more than 100 wind turbines and are characterized by complex boundaries due to shipping lanes, neighboring wind farms, and other constraints. Layout optimization methods are broadly split between gradient-based and gradient-free approaches. Gradient-based approaches can converge quickly and perform well for smaller, academic problems but are often sensitive to initial conditions and tuning parameters and require expert knowledge to use. On the other hand, gradient-free approaches can be more robust to problem complexities. We present a robust layout optimization approach based on a random search algorithm. The algorithm is intended for those who are not optimization experts and has few tuning parameters that need specification to achieve satisfactory results. Unlike off-the-shelf methods, which use generally available, non-domain-specific optimization routines that accept as inputs an optimization function and constraint definitions, this approach takes advantage of the relative computational costs of the different evaluations by evaluating cheaper computations first (boundary and minimum distance constraints) and running expensive AEP evaluations only if all other checks pass. Moreover, an outer genetic algorithm allows multiple solutions to evolve in parallel, enabling rapid solution development on high-performance computers. We discuss the relative ease of selecting necessary tuning parameters and demonstrate the efficacy of the genetic random search on a complex layout problem consisting of placing 70 turbines in a nonconvex and unconnected boundary region.

17 WIND ENERGY↗
DOE OSTI2020

Study of space charge in the ICARUS T600 detector

The accumulation of positive ions, produced by ionizing particles crossing Liquid Argon Time Projection Chambers (LAr-TPCs), may generate distortions of the electric drift field affecting the track reconstruction of the ionizing events. These effects could become relevant for large LAr-TPCs operating at surface or at shallow depth, where the detectors are exposed to a copious flux of cosmic rays. We report a detailed study of such possible field distortions in the ICARUS T600 LAr-TPC has been performed analyzing a sample of cosmic muon tracks recorded with one T600 module operated at surface in 2001. The maximum track distortion turns out to be of few mm in good agreement with the prediction by a numerical calculation. As a cross-check, the same analysis has been performed on a cosmic muon sample recorded during the ICARUS T600 run at the LNGS underground laboratory, where the cosmic ray flux was suppressed by a factor $\sim 10^6$ by 3400 m water equivalent shielding. No appreciable distortion has been observed, confirming that the effects measured on surface are actually due to ion space charge.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

A new calibration method for charm jet identification validated with proton-proton collision events at $\sqrt{s}$ =13 TeV

Many measurements at the LHC require efficient identification of heavy-flavour jets, i.e. jets originating from bottom (b) or charm (c) quarks. An overview of the algorithms used to identify c jets is described and a novel method to calibrate them is presented. This new method adjusts the entire distributions of the outputs obtained when the algorithms are applied to jets of different flavours. It is based on an iterative approach exploiting three distinct control regions that are enriched with either b jets, c jets, or light-flavour and gluon jets. Results are presented in the form of correction factors evaluated using proton-proton collision data with an integrated luminosity of 41.5 fb$^{-1}$ at √s = 13 TeV, collected by the CMS experiment in 2017. The closure of the method is tested by applying the measured correction factors on simulated data sets and checking the agreement between the adjusted simulation and collision data. Furthermore, a validation is performed by testing the method on pseudodata, which emulate various mismodelling conditions. The calibrated results enable the use of the full distributions of heavy-flavour identification algorithm outputs, e.g. as inputs to machine-learning models. Thus, they are expected to increase the sensitivity of future physics analyses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

ATLAS ITk strip sensor quality control procedures and testing site qualification

Abstract The high-luminosity upgrade of the Large Hadron Collider, scheduled to become operational in 2029, requires the replacement of the ATLAS Inner Detector with a new all-silicon Inner Tracker. Radiation hard n + -in-p micro-strip silicon sensors were developed by the ATLAS Inner Tracker strip collaboration and are produced by Hamamatsu Photonics K.K. Production of the total amount of 22000 strip sensors has started in 2020 and will continue until 2025. The ATLAS strip sensor collaboration has the responsibility to monitor the quality of the fabricated devices by performing detailed measurements of individual sensor characteristics and by comparing the obtained results with the tests done by the manufacturer. Dedicated Quality Control procedures were developed to check whether the delivered large-format sensors adhere to the ATLAS specifications. The institutes performing the Quality Control testing of the pre-production and production ATLAS ITk strip sensors had to initially be qualified for multiple high-throughput tests by successfully completing the Site Qualification process. The Quality Control procedures and the qualification process are described in this paper.

Instruments & Instrumentation↗
DOE OSTI2023

Reflectance and fluorescence characteristics of PTFE coated with TPB at visible, UV, and VUV as a function of thickness

Polytetrafluoroethylene (PTFE) is an excellent diffuse reflector widely used in light collection systems for particle physics experiments. In noble element systems, it is often coated with tetraphenyl butadiene (TPB) to allow detection of vacuum ultraviolet scintillation light. Here, in this work this dependence is investigated for PTFE coated with TPB in air for light of wavelengths of 200 nm, 260 nm, and 450 nm. The results show that TPB-coated PTFE has a reflectance of approximately 92% for thicknesses ranging from 5 mm to 10 mm at 450 nm, with negligible variation as a function of thickness within this range. A cross-check of these results using an argon chamber supports the conclusion that the change in thickness from 5 mm to 10 mm does not affect significantly the light response at 128 nm. Our results indicate that pieces of TPB-coated PTFE thinner than the typical 10 mm can be used in particle physics detectors without compromising the light signal.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Establishing the Quality Assurance programme for the strip sensor production of the ATLAS tracker upgrade including irradiation with neutrons, photons and protons to HL-LHC fluences

The successful pre-production delivery of strip sensors for the new Inner Tracker (ITk) for the upgraded ATLAS detector at the High Luminosity LHC (HL-LHC) at CERN was completed and based on their performance full production has commenced. The overall delivery period is anticipated to last 4 years to complete the approximately 22000 sensors required for the ITk. For Quality Assurance (QA), a number of test structures designed by the collaboration, along with a large area diode and miniature version of the main sensor, are produced in every wafer by the foundry Hamamatsu Photonics K.K (HPK). As well as Quality Control (QC) checks on every main sensor, samples of the QA pieces from each delivery batch are tested both before and after irradiation with results after exposure to neutrons, gammas or protons to fluences and doses corresponding to those anticipated after operation at the HL-LHC to roughly 1.5 times the ultimate integrated luminosity of 4000 fb -1 . In this paper the procedures are presented and the studies carried out to establish that the seven ITk QA Strip Sensor irradiation and test sites meet all the requirements to support this very extensive programme throughout the strip sensor production phase for the ITk project.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Setups for eliminating static charge of the ATLAS18 strip sensors

Abstract Construction of the new all-silicon Inner Tracker (ITk), developed by the ATLAS collaboration to beable to track charged particles produced at the High-Luminosity LHC, started in 2020 and is expected tocontinue till 2028. The ITk detector will include 18,000 highly segmented and radiation hard n+-in-psilicon strip sensors (ATLAS18), which are being manufactured by Hamamatsu Photonics. Mechanical and electrical characteristics of produced sensors are measured upon their delivery at several institutes participating in a complex Quality Control (QC) program. The QC tests performed on each individual sensor check the overall integrity and quality of the sensor.During the QC testing of ATLAS18 strip sensors, an increased number of sensors thatfailed the electrical tests was observed. In particular, IV measurements indicated an early breakdown,while large areas containing several tens or hundreds of neighbouring strips with low interstrip isolationwere identified by the Full strip tests, and leakage current instabilities were measured in a long-term leakage current stability setup. Moreover, a high surface electrostatic charge reaching a level of several hundreds of volts per inch was measured on a large number of sensors and on the plastic sheets, whichmechanically protect these sensors in their paper envelopes. Accumulated data indicates a clearcorrelation between observed electrical failures and the sensor charge-up.To mitigate the above-described issues, the QC testing sites significantly modified the sensor handlingprocedures and introduced sensor recovery techniques based on irradiation of the sensor surface with UVlight or application of intensive flows of ionized gas. In this presentation, we will describe the setupsimplemented by the QC testing sites to treat silicon strip sensors affected by static charge andevaluate the effectiveness of these setups in terms of improvement of the sensor performance.

Instruments & Instrumentation↗
DOE OSTI2025

Proton reconstruction with the TOTEM Roman pot detectors for high- β * LHC data

The TOTEM Roman pot detectors are used to reconstruct the transverse momentum of scattered protons and to estimate the transverse location of the primary interaction. This paper presents new methods of track reconstruction, measurements of strip-level detection efficiencies, cross-checks of the LHC beam optics, and detector alignment techniques, along with their application in the selection of signal collision events. The track reconstruction is performed by exploiting hit cluster information through a novel method using a common polygonal area in the intercept-slope plane. The technique is applied in the relative alignment of detector layers with μm precision. A tag-and-probe method is used to extract strip-level detection efficiencies. The alignment of the Roman pot system is performed through time-dependent adjustments, resulting in a position accuracy of 3 μm in the horizontal and 60 μm in the vertical directions. The goal is to provide an optimal reconstruction tool for central exclusive physics analyses based on the high-β* data-taking period at $\sqrt({s})$ = 13 TeV in 2018.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Electromagnetic energy calibration of the SoLid detector with horizontal muons

SoLid is a neutrino experiment at very-short baselinesearching for active-to-sterile oscillations of reactorantineutrinos. The detection principle is based on the pairing oftwo types of solid scintillators: polyvinyl toluene and $^{6}$Li:ZnS(Ag), which is a new technology used in this field ofPhysics. In addition to good neutron-gamma discrimination, thissetup allows the detector to be highly segmented; the basicdetection unit is a 5 cm cube. High segmentation provides numerousadvantages including precise localisation of the Inverse Beta Decay(IBD) products, the derivation of an antineutrino energy estimatorbased on the isolated positron energy, and a powerful backgroundreduction tool that relies on the topological signature of thesignal. Finally, the system is read out by a network ofwavelength-shifting fibres coupled to photosensors. A relativeelectromagnetic calibration is performed with horizontal cosmicmuons. This source poses the simplest calibration problem in which asingle detection unit is involved. In addition, large muon energydeposits allow us to perform a calibration at the most detailedlevel (i.e. per fibre) and to accurately define the fraction ofenergy escaping to neighbouring detection cells. A statisticalprecision at the sub-percent level is reached. The paper alsodiscusses two methods to calibrate the absolute energy scale andpresents their implementation and results. The first method relieson horizontal muons, though the precision is limited to around 10%because of the uncertainty in the energy distribution of suchmuons. A novel, alternative method based on the radioactiveamericium-beryllium source is proposed. It takes advantage of theelectron-positron pair-production process and provides a calibrationpoint at 3.4 MeV (i.e. in the core of the IBD positronspectrum). The paper is concluded with various cross-check includinga determination of the energy spectrum of the standard cosmogenicbackground candle: $^{12}$B.

Abreu, Y. [Antwerp U.]↗
DOE OSTI2026

Diagnosing the representation of surface and layered soil moisture in Earth system models

Surface soil moisture (mrsos) and vertically integrated soil moisture (mrsol) over the top 10 cm should, by definition, be physically consistent in Earth System Models (ESMs). However, an evaluation of nine CMIP6 models reveals substantial inconsistencies: in some models, mrsos and integrated mrsol agree globally; in others, they align only in specific regions; and in a few, they diverge across all grid cells. These discrepancies arise from a combination of factors, including metadata errors, inconsistent variable definitions, or diagnostic sequencing within the model. We demonstrate how such issues can lead to significant biases, even when both variables are present and seemingly well-defined. As model complexity increases and multi-model comparisons become more common, assumptions about variable equivalence may lead to flawed conclusions. This study highlights the need for routine consistency checks, improved metadata standards, and community-wide practices that ensure reliability of derived variables across ESM outputs, particularly in preparation for CMIP7.

Earth system models↗
DOE OSTI2022

Circuit complexity near critical points

Here, we consider the Bose–Hubbard model in two and three spatial dimensions and numerically compute the quantum circuit complexity of the ground state in the Mott insulator and superfluid phases using a mean field approximation with additional quadratic fluctuations. After mapping to a qubit system, the result is given by the complexity associated with a Bogoliubov transformation applied to the reference state taken to be the mean field ground state. In particular, the complexity has peaks at the O(2) critical points where the system can be described by a relativistic quantum field theory. Given that we use a Gaussian approximation, near criticality the numerical results agree with a free field theory calculation. To go beyond the Gaussian approximation we use general scaling arguments that imply that, as we approach the critical point t → t c , there is a non-analytic behavior in the complexity c 2 (t) of the form |c 2 (t) – c 2 (t c )| ~ |t – t c | νd , up to possible logarithmic corrections. Here d is the number of spatial dimensions and ν is the usual critical exponent for the correlation length ξ ~ |t – t c | –ν . As a check, for d = 2 this agrees with the numerical computation if we use the Gaussian critical exponent $v=\frac{1}{2}$. Finally, using AdS/CFT methods, we study higher dimensional examples and confirm this scaling argument with non-Gaussian exponent ν for strongly interacting theories that have a gravity dual.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗