David Anthony Clarke

We develop a one-class, deep-learning framework to detect the phase transition and recover critical behavior of the three-dimensional (3D) Ising model. A 3D convolutional 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 ) , in excellent agreement with the known value. Additionally, we obtain an estimate of the correlation-length critical exponent, ν = 0.63 ( 27 ) , also 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.

We introduce a generalized definition of the isothermal compressibility ( κ T , σ Q 2 ) calculable by keeping net conserved charge fluctuations rather than total number densities constant. We present lattice QCD results for this isothermal compressibility, expressed in terms of fluctuations of conserved charges that are related to baryon ( B ), electric charge ( Q ), and strangeness ( S ) quantum numbers. This generalized isothermal compressibility is compared with hadron resonance gas model calculations as well as with heavy-ion collision data obtained at RHIC and the LHC. We find κ T , σ Q 2 = 13.8 ( 1.3 ) fm 3 / GeV at T pc , 0 = 156.5 ( 1.5 ) MeV and μ ^ B = 0 . This finding is consistent with the rescaled result of the ALICE Collaboration, where we replaced the number of charged hadrons ( N ch ) by the total number of hadrons ( N tot ) at freeze-out. Normalizing this result with the QCD pressure ( P ) we find that the isothermal compressibility on the pseudocritical line stays close to that of an , i.e., P κ T , σ Q 2 ≃ 1 .

Using the multipoint Padé approach, we locate Lee-Yang edge singularities of the quantum chromodynamics (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 end point, we extrapolate the singularities on N τ = 6 lattices to pure real baryon chemical potential to estimate the position of the critical end point (CEP). We find T CEP = 10 2 − 23 + 11 MeV and μ B CEP = 42 8 − 74 + 162 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 ( 20 ) .

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_{c} behaves similarly to an order parameter, and this analogy has been successfully used to locate T_{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 two-dimensional Ising model when the network is trained on configurations at T=0 and T=∞ only. We directly compare its output to the same network trained at multiple temperatures below and above T_{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_{c} and ν, while the extraction of γ becomes more challenging.

We present results for the dominant light-quark connected contribution to the long-distance window of the hadronic vacuum polarization (HVP) contribution to the muon g − 2 from lattice quantum chromodynamics. 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 a μ l l , LD ( conn ) = 400.2 ( 2.3 ) stat ( 3.7 ) syst [ 4.3 ] total × 10 − 10 . Summing this result with our recent determinations of the light-quark connected contributions to the short- and intermediate-distance windows, we obtain a subpercent precision determination of the light-quark-connected contribution to HVP of a μ l l ( conn ) = 655.2 ( 2.3 ) stat ( 3.9 ) syst [ 4.5 ] total × 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.

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 μ l l , SD ( conn ) = 48.139 ( 11 ) stat ( 91 ) syst [ 92 ] total × 10 − 10 and a μ l l , W ( conn ) = 206.90 ( 14 ) stat ( 61 ) syst [ 63 ] total × 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 μ SD = 69.05 ( 1 ) stat ( 21 ) syst [ 21 ] total × 10 − 10 and a μ W = 236.45 ( 17 ) stat ( 83 ) syst [ 85 ] total × 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. Published by the American Physical Society 2025