arXiv subjects

David A. Clarke

Publications and source records attributed to David A. Clarke.

17 recordsLinked to original sources

arXiv2026

Hadronic contributions to $α(Q^{2})$ and $\sin^{2}θ_{W}(Q^{2})$ from spectral reconstruction of lattice-QCD data

We present preliminary results from a lattice-QCD study of the hadronic contributions to the running of the electromagnetic coupling, $Δα(Q^2)$, and the electroweak mixing angle, $Δ\sin^2θ_{W}(Q^2)$. Using $N_f = 2+1+1$ HISQ ensembles at physical quark masses, we discuss the challenges posed by strong statistical correlations in the time-momentum representation and propose a spectral-reconstruction strategy to obtain controlled continuum-extrapolated results across the full energy range.

hep-lat↗

arXiv2026

Detecting the 3D Ising model phase transition with a ground-state-trained autoencoder

We develop a one-class, deep-learning framework to detect the phase transition and recover critical behavior of the 3D Ising model. A 3D convolutional neural network autoencoder (CAE) is trained on ground-state configurations only, without prior knowledge of the critical temperature, the Hamiltonian, or the order parameter. After training, the model is applied to Monte Carlo configurations across a wide temperature range and different lattice sizes. The mean-square reconstruction error is shown to be sensitive to the transition. Finite-size scaling of the peak location for the reconstruction error susceptibility yields the critical temperature $T_c=4.5128(58)$ and the correlation-length critical exponent $ν=0.63(27)$, consistent with results from the literature. Our results show that a one-class CAE, trained on zero-temperature configurations only, can recover nontrivial critical behavior of the 3D Ising model.

cond-mat.stat-mech↗

arXiv2025

High-Precision Scale Setting with the Omega-Baryon Mass and Gradient Flow

The gradient-flow scale $w_0$ in lattice QCD is determined using the mass of the $Ω^-$ baryon to set the physical scale. Nine ensembles using the highly improved staggered quark (HISQ) action with lattice spacings of 0.15 fm down to 0.04 fm are used, seven of which have nearly physical light-quark masses. Electromagnetic corrections to the $Ω^-$ mass are defined in order to compute a pure-QCD $Ω$ mass. The final result is $w_0 = 0.17187(68)$ fm, corresponding to a relative uncertainty of 0.40% and a central value in good agreement with previous calculations in the literature.

hep-lat↗

arXiv2025

Deep learning of phase transitions with minimal examples

Over the past several years, there have been many studies demonstrating the ability of deep neural networks to identify phase transitions in many physical systems, notably in classical statistical physics systems. One often finds that the prediction of deep learning methods trained on many ensembles below and above the critical temperature $T_{\rm c}$ behaves similarly to an order parameter, and this analogy has been successfully used to locate $T_{\rm c}$ and estimate universal critical exponents. In this work, we pay particular attention to the ability of a convolutional neural network to capture these critical parameters for the 2-$d$ Ising model when the network is trained on configurations at $T=0$ and $T=\infty$ only. We directly compare its output to the same network trained at multiple temperatures below and above $T_{\rm c}$ to gain understanding of how this extreme restriction of training data can impact a neural network's ability to classify phases. We find that the network trained on two temperatures is still able to identify $T_{\rm c}$ and $ν$, while the extraction of $γ$ becomes more challenging.

cond-mat.stat-mech↗

arXiv2025

Hadronic vacuum polarization for the muon $g-2$ from lattice QCD: Long-distance and full light-quark connected contribution

We present results for the dominant light-quark connected contribution to the long-distance window (LD) of the hadronic vacuum polarization contribution (HVP) to the muon $g-2$ from lattice quantum chromodynamics (QCD). Specifically, with a new determination of the lattice scale on MILC's physical-mass HISQ ensembles, using the $Ω^-$ baryon mass, we obtain a result of $400.2(2.3)_{\mathrm{stat}}(3.7)_{\mathrm{syst}}[4.3]_{\mathrm{total}} \times 10^{-10}$. Summing this result with our recent determinations of the light-quark connected contributions to the short- (SD) and intermediate-distance (W) windows, we obtain a sub-percent precision determination of the light-quark-connected contribution to HVP of $655.5(2.3)_{\mathrm{stat}}(3.9)_{\mathrm{syst}}[4.5]_{\mathrm{total}} \times 10^{-10}$. Finally, as a consistency check, we verify that an independent analysis of the full contribution is in agreement with the sum of individual windows. We discuss our future plans for improvements of our HVP calculations to meet the target precision of the Fermilab $g-2$ experiment.

hep-lat↗

arXiv2025

Hadronic vacuum polarization for the muon $g-2$ from lattice QCD: Complete short and intermediate windows

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment $a_μ$ in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to $a_μ$, respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong isospin-breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark connected contribution, we obtain $a^{ll,\,{\mathrm{SD}}}_μ(\mathrm{conn.}) = 48.139(11)_{\mathrm{stat}}(91)_{\mathrm{syst}}[92]_{\mathrm{total}} \times 10^{-10}$ and $a^{ll,\,{\mathrm{W}}}_μ(\mathrm{conn.}) = 206.90(14)_{\mathrm{stat}}(61)_{\mathrm{syst}}[63]_{\mathrm{total}} \times 10^{-10}$. We use Bayesian model averaging to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are $a^{\mathrm{SD}}_μ = 69.05(1)_{\mathrm{stat}}(21)_{\mathrm{syst}}[21]_{\mathrm{total}} \times 10^{-10}$ and $a^{\mathrm{W}}_μ = 236.45(17)_{\mathrm{stat}}(83)_{\mathrm{syst}}[85]_{\mathrm{total}} \times 10^{-10}$. This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few permille level.

hep-lat↗

arXiv2024

Searching for the QCD critical endpoint using multi-point Padé approximations

Using the multi-point Padé approach, we locate Lee-Yang edge singularities of the QCD pressure in the complex baryon chemical potential plane. These singularities are extracted from singularities in the net baryon-number density calculated in $N_f=2+1$ lattice QCD at physical quark mass and purely imaginary chemical potential. Taking an appropriate scaling ansatz in the vicinity of the conjectured QCD critical endpoint, we extrapolate the singularities on $N_τ=6$ lattices to pure real baryon chemical potential to estimate the position of the critical endpoint (CEP). We find $T^{\rm CEP}=105^{+8}_{-18}$~ MeV and $μ_B^{\rm CEP} = 422^{+80}_{-35}$~ MeV, which compares well with recent estimates in the literature. For the slope of the transition line at the critical point we find $-0.16(24)$.

hep-lat↗

arXiv2024

SIMULATeQCD: A simple multi-GPU lattice code for QCD calculations

The rise of exascale supercomputers has fueled competition among GPU vendors, driving lattice QCD developers to write code that supports multiple APIs. Moreover, new developments in algorithms and physics research require frequent updates to existing software. These challenges have to be balanced against constantly changing personnel. At the same time, there is a wide range of applications for HISQ fermions in QCD studies. This situation encourages the development of software featuring a HISQ action that is flexible, high-performing, open source, easy to use, and easy to adapt. In this technical paper, we explain the design strategy, provide implementation details, list available algorithms and modules, and show key performance indicators for SIMULATeQCD, a simple multi-GPU lattice code for large-scale QCD calculations, mainly developed and used by the HotQCD collaboration. The code is publicly available on GitHub.

hep-lat↗

arXiv2024

Universal scaling and the asymptotic behaviour of Fourier coefficients of the baryon-number density in QCD

We discuss the scaling of the Yang-Lee singularity (YLs) and show how the universal scaling can be used to locate phase transitions in QCD. We describe two complementary methods to extract the location of the Yang-Lee singularity from lattice QCD data of the baryon-number density and higher order cumulants of the baryon number, obtained at imaginary chemical potential. The first method (multi-point Padé resummation) is used to determine the Roberge-Weiss phase transition temperature. Our continuum extrapolated result is $T_{RW}=211.1\pm3.1$ MeV. The second method is based on the asymptotic behaviour of the Fourier coefficients of the baryon-number density. We discuss the derivation of a fitting function and demonstrate that the procedure can successfully locate the YLs in the Quark Meson model.

hep-lat↗

arXiv2023

Determination of Lee-Yang edge singularities in QCD by rational approximations

We report updated results on the determination of Lee-Yang edge (LYE) singularities in $N_f = 2+1$ QCD using highly improved staggered quarks (HISQ) with physical masses on $N_τ= 4, 6, 8$ lattices. The singularity structure of QCD in the complex $μ_B$ plane is probed using conserved charges calculated at imaginary $μ_B$. The location of the singularities is determined by studying the (uncancelled) poles of multi-point Padé approximants. We show that close to the Roberge-Weiss (RW) transition, the location of the LYE singularities scales according to the $3$-$d$ $Z(2)$ universality class. By combining the new $N_τ= 6$ data with the $N_τ= 4$ data from our previous analysis we extract a rough estimate for the RW temperature in the continuum limit. We also discuss some preliminary results for the singularities close to the chiral phase transition obtained from simulations on $N_τ= 6, 8$ lattices.

hep-lat↗

arXiv2022

Detecting critical points from Lee-Yang edge singularities in lattice QCD

A new approach is presented to explore the singularity structure of lattice QCD in the complex chemical potential plane. Our method can be seen as a combination of the Taylor expansion and analytic continuation approaches. Its novelty lies in using rational (Padé) approximants for studying Lee-Yang edge singularities. We present a calculation of the cumulants of the net-baryon number as a function of a purely imaginary baryon number chemical potential, obtained with highly improved staggered quarks at temporal lattice extent of $N_τ=4,6$. We construct various rational function approximations of the lattice data and determine their poles (and roots) in the complex plane. We compare the position of the closest pole to the theoretically expected position of the Lee-Yang edge singularity. At high temperature, we find scaling that is in accordance with the expected power law behavior of the Roberge-Weiss transition while a different behavior is found for $T\lesssim 170$ MeV.

hep-lat↗

arXiv2020

Polyakov Loop Susceptibility and Correlators in the Chiral Limit

In quenched QCD the Polyakov loop is an order parameter of the deconfinement transition, but with decreasing quark mass, the peak in the Polyakov loop susceptibility becomes less pronounced, and it loses its interpretation as an indicator for deconfinement. For this $N_f=2+1$ HISQ study, we fix the strange quark mass $m_s$ at its physical value and investigate the dependence of the Polyakov loop on the light quark mass $m_l$ in the range $m_s/m_l=27-160$, following $m_l$ toward the chiral limit. In particular we will look how the inflection point and susceptibility behave as we decrease $m_l$, to see whether one finds any indication of a crossover, and therefore whether the Polyakov loop is sensitive to the chiral phase transition. Preliminary results show no signal of a crossover from the real part of the Polyakov loop in the vicinity of the chiral crossover. Closely related is an investigation of Polyakov loop correlations and the Debye mass in this limit. Preliminary results suggest little or no dependence on $m_l$.

hep-lat↗

arXiv2019

Topological charge and cooling scales in pure SU(2) lattice gauge theory

Using Monte Carlo simulations with overrelaxation, we have equilibrated lattices up to $β=2.928$, size $60^4$, for pure SU(2) lattice gauge theory with the Wilson action. We calculate topological charges with the standard cooling method and find that they become more reliable with increasing $β$ values and lattice sizes. Continuum limit estimates of the topological susceptibility $χ$ are obtained of which we favor $χ^{1/4}/T_c=0.643\,(12)$, where $T_c$ is the SU(2) deconfinement temperature. Differences between cooling length scales in different topological sectors turn out to be too small to be detectable within our statistical errors.

hep-lat↗

arXiv2019

MHD simulations of the formation and propagation of protostellar jets to observational length scales

We present 2.5-D global, ideal MHD simulations of magnetically and rotationally driven protostellar jets from Keplerian accretion discs, wherein only the initial magnetic field strength at the inner radius of the disc, $B_{\rm i}$, is varied. Using the AMR-MHD code AZEUS, we self-consistently follow the jet evolution into the observational regime ($>10^3\,\mathrm{AU}$) with a spatial dynamic range of $\sim6.5\times10^5$. The simulations reveal a three-component outflow: 1) A hot, dense, super-fast and highly magnetised 'jet core'; 2) a cold, rarefied, trans-fast and highly magnetised 'sheath' surrounding the jet core and extending to a tangential discontinuity; and 3) a warm, dense, trans-slow and weakly magnetised shocked ambient medium entrained by the advancing bow shock. The simulations reveal power-law relationships between $B_{\rm i}$ and the jet advance speed, $v_{\rm jet}$, the average jet rotation speed, $\langle v_φ\rangle$, as well as fluxes of mass, momentum, and kinetic energy. Quantities that do not depend on $B_{\rm i}$ include the plasma-$β$ of the transported material which, in all cases, seems to asymptote to order unity. Jets are launched by a combination of the 'magnetic tower' and 'bead-on-a-wire' mechanisms, with the former accounting for most of the jet acceleration---even for strong fields---and continuing well beyond the fast magnetosonic point. At no time does the leading bow shock leave the domain and, as such, these simulations generate large-scale jets that reproduce many of the observed properties of protostellar jets including their characteristic speeds and transported fluxes.

astro-ph.SR↗

arXiv2016

Deconfinement, gradient and cooling scales for pure SU(2) lattice gauge theory

We investigate the approach of pure SU(2) lattice gauge theory with the Wilson action to its continuum limit using the deconfining phase transition, the gradient flow and the cooling flow to set the scale. For the gradient and cooling scales we explore three different energy observables and two distinct reference values for the flow time. When the aim is to follow scaling towards the continuum limit, one gains at least a factor of 100 in computational efficiency by relying on the gradient instead of the deconfinement scale. Using cooling instead of the gradient flow one gains another factor of at least 34 in computational efficiency on the gradient flow part without any significant loss in the accuracy of scale setting. Concerning our observables, the message is to keep it simple. The Wilson action itself performs as well as or even better than the other two observables explored. Two distinct fitting forms for scaling are compared of which one connects to asymptotic scaling. Differences of the obtained estimates show that systematic errors of length ratios, though only about 1%, can be considerably larger than statistical errors of the same observables.

hep-lat↗

arXiv2011

AZEuS: An Adaptive Zone Eulerian Scheme for Computational MHD

A new adaptive mesh refinement (AMR) version of the ZEUS-3D astrophysical magnetohydrodynamical (MHD) fluid code, AZEuS, is described. The AMR module in AZEuS has been completely adapted to the staggered mesh that characterises the ZEUS family of codes, on which scalar quantities are zone-centred and vector components are face-centred. In addition, for applications using static grids, it is necessary to use higher-order interpolations for prolongation to minimise the errors caused by waves crossing from a grid of one resolution to another. Finally, solutions to test problems in 1-, 2-, and 3-dimensions in both Cartesian and spherical coordinates are presented.

astro-ph.IM↗

arXiv2010

Simulating protostellar jets simultaneously at launching and observational scales

We present the first 2.5-D MHD simulations of protostellar jets that include both the region in which the jet is launched magnetocentrifugally at scale lengths $<0.1$ AU, and where the propagating jet is observed at scale lengths $>10^3$ AU. These simulations, performed with the new AMR-MHD code AZEuS, reveal interesting relationships between conditions at the disc surface, such as the magnetic field strength, and direct observables such as proper motion, jet rotation, jet radius, and mass flux. By comparing these quantities with observed values, we present direct numerical evidence that the magnetocentrifugal launching mechanism is capable, by itself, of launching realistic protostellar jets.

astro-ph.SR↗