arXiv subjects

Gert Aarts

Publications and source records attributed to Gert Aarts.

At least 19 recordsLinked to original sources

arXiv2026

Future Requirements of Lattice Field Theory Calculations on European High-Performance Computing Facilities

Lattice field theory provides a first-principles framework for studying properties of strongly interacting quantum field theories in elementary particle physics. Researchers in lattice field theory are also among the largest and most efficient users of high- performance computing resources in fundamental science. In this contribution, we outline the computational profile of lattice QCD, from gauge-field generation to large-scale measurements, and discuss the main hardware, software, and human resource requirements needed to sustain progress on current and future European HPC infrastructures.

hep-lat↗

arXiv2026

Diffusion Models for Sampling Near Criticality in Lattice Field Theories

We investigate generative diffusion models as denoising samplers for two- and three-dimensional lattice $\phi^4$ theory across the symmetric, near-critical, and broken phases. Validated against ensembles generated by Fourier-accelerated HMC combined with Wolff cluster updates, the reverse-SDE sampler reproduces scalar observables and the momentum-space propagator $G(|k|)$, with residual bias concentrated in the zero-mode and, in three dimensions, the action density. We introduce two local diagnostics and an HMC-referenced effective sample size (ESS), which probe the learned drift directly, through a Metropolis-adjusted Langevin acceptance rate, and through observable-level bias and variance. Exploiting a fully convolutional architecture with weights shared across different volumes ($V=L^D$), we show that cross-volume training transfers to unseen sizes, matching or slightly improving in-distribution training in the two-dimensional symmetric and broken phases. A three-dimensional model trained on $L \in \{4, 8, 16, 32\}$ reproduces the propagator and most scalar observables at the unseen lattice size $L = 64$ across the phase diagram, with the residual susceptibility excess in the broken phase as the main exception, and improves several critical observables relative to in-distribution $L = 64$ training. This establishes cross-volume generalization as a viable mechanism for large-volume sampling, and the score learned from many cheap small-lattice configurations transfers to the target volume without retraining.

hep-lat↗

arXiv2026

Spectral phase transitions and trainability in neural network learning dynamics

The emergence of low-dimensional structures in the spectra of neural network weight matrices is a common empirical feature of trained models, but the dynamical origin of this phenomenon during learning remains an open problem. We formulate neural network training as the stochastic evolution of an initially random matrix ensemble, driven by stochastic gradient descent (SGD) updates that reshape the spectral bulk while amplifying signal strength. This induces a Baik-Ben Arous-P\'ech\'e (BBP) transition during training, where isolated eigenvalues detach from the random bulk distribution, providing a dynamical framework for representation formation in high-dimensional learning dynamics. We demonstrate this in a solvable linear teacher-student model, where spectral evolution is analytically tractable and a phase diagram of trainability governed by the step size (or learning rate) and initial weight variance is obtained, and subsequently extend our formalism beyond the linear regime to nonlinear and stochastic settings. Numerical simulations in realistic settings support this picture, showing robust emergence of spectral alignment during training. Our results suggest that spectral analysis may provide a unified perspective of stochastic learning dynamics, linking trainability, optimisation hyperparameters, spectral phase transitions, and representation learning in neural networks.

cond-mat.dis-nn↗

arXiv2026

Stochastic Path Sampler For Lattice Field Theory

In lattice field theory, target distributions are known only up to normalization, (\tilde{\pi}(\phi)\propto e^{-S(\phi)}), while the partition function is intractable. Markov chain Monte Carlo simulations often become inefficient near phase transitions or the continuum limit due to critical slowing down. In this work, we propose a novel sampler based on nonequilibrium thermodynamics, called Stochastic Path Sampler (SPS), which can generate configurations for the unnormalized target distribution without requiring training data. The central idea of SPS is to establish a trajectory-level balance for learnable forward and backward stochastic dynamics between two equilibrium states, namely the prior and target distributions. This is achieved by minimizing the path-space variational free energy, equivalently an entropy-production upper bound, defined by the log-ratio of forward and auxiliary backward trajectory measures, thereby enhancing the reversibility of the forward and backward processes. The learned forward process provides independent proposals, which are subsequently corrected by an extended-space Independence Metropolis--Hastings step. In two-dimensional (\phi^4) theory, we demonstrate that our neural sampler can achieve the same sampling quality as HMC but with a much shorter autocorrelation time in the critical region. This sampler offers a stochastic-quantization-inspired route to data-free proposal construction for lattice field theory by leveraging a variational free-energy principle derived from path-space irreversibility.

hep-lat↗

arXiv2026

Lattice field theories with a sign problem

The sign problem obstructs the determination of the QCD phase diagram in the temperature-baryon chemical potential plane using lattice QCD. We review the sign problem in QCD and related field theories, including applications to real-time dynamics. We focus on approaches where the sign problem can potentially be solved or controlled, irrespective of its severeness. These include holomorphic extensions -- Lefschetz thimbles, holomorphic flow, contour deformations, and complex Langevin dynamics --, and the introduction of new degrees of freedom -- dual variables and the tensor renormalisation group. We also highlight directions in which machine learning approaches have shown promise. Since many methods are first tested in simpler models, we provide an outlook on their feasibility for lattice systems.

hep-lat↗

arXiv2026

Heavy quark thermodynamics with anisotropic lattices

We present recent results from the FASTSUM collaboration, using anisotropic lattice QCD to study spectral properties of heavy quarkonia and open heavy flavour systems at high temperature. For heavy quarkonium, our results using a number of different methods suggest a small but significant and robust negative mass shift as well as an increasing thermal width. We present the first lattice results for masses and spectral functions of B mesons at high temperature, and preliminary results for a high-precision calculation of the static quark potential.

hep-lat↗

arXiv2026

On the effective restoration of $U(1)_A$ symmetry at finite temperature

The $U(1)_A$ symmetry of the massless QCD Lagrangian is explicitly broken by the axial anomaly, but it may be effectively restored at finite temperature. Determining the temperature at which this occurs is important for understanding the chiral transition and the structure of the QCD phase diagram. A commonly used probe of effective $U(1)_A$ restoration is the degeneracy of flavour non-singlet pseudoscalar and scalar susceptibilities. Using anisotropic lattice QCD ensembles with Wilson-clover fermions generated by the \textsc{Fastsum} collaboration, we study this degeneracy through hadronic correlation functions over a wide range of temperatures. The fine temporal resolution of our Generation 3 ensembles allows us to determine the temperature at which the pseudoscalar and scalar channels become degenerate. We find evidence for the effective restoration of $U(1)_A$ symmetry at $T_{U(1)_A}=319(22)$ MeV, well above the chiral crossover temperature.

hep-lat↗

arXiv2026

$U(1)_A$ symmetry restoration at finite temperature with mesonic correlators

The $U(1)_A$ symmetry of the massless QCD Lagrangian is explicitly broken in the quantised theory by the anomaly. It may be effectively restored at some finite temperature, which would have important consequences for the order of the chiral transition and the QCD phase diagram. It has been argued in the literature that one way to probe the effective restoration of $U(1)_A$ is to check for the degeneracy of pseudoscalar and flavour non-singlet scalar correlators. In this work, we consider a new method of examining this degeneracy based upon hadron correlation functions on the anisotropic FASTSUM ensembles. The anisotropic nature and our newest Generation 3 ensembles aid in a determination of the effective restoration of the $U(1)_A$ symmetry which we find to be $T_{U(1)_A} \sim 320$ MeV, well above the chiral transition temperature, which is $T_{\rm pc} \sim 180$ MeV for our choice of Wilson-Clover fermions.

hep-lat↗

arXiv2026

Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory

We demonstrate that gauge equivariant diffusion models can accurately model the physics of non-Abelian lattice gauge theory using the Metropolis-adjusted annealed Langevin algorithm (MAALA), as exemplified by computations in two-dimensional U(2) and SU(2) gauge theories. Our network architecture is based on lattice gauge equivariant convolutional neural networks (L-CNNs), which respect local and global symmetries on the lattice. Models are trained on a single ensemble generated using a traditional Monte Carlo method. By studying Wilson loops of various size as well as the topological susceptibility, we find that the diffusion approach generalizes remarkably well to larger inverse couplings and lattice sizes with negligible loss of accuracy while retaining moderately high acceptance rates.

hep-lat↗

arXiv2025

Approaching the continuum with anisotropic lattice thermodynamics

The FASTSUM collaboration has a long-standing programme of using anisotropic lattice QCD to investigate strong interaction thermodynamics, and in particular spectral quantities. Here we present first results from our new ensemble which has a temporal lattice spacing a_t=15am and anisotropy xi=a_s/a_t=7, giving unprecedented resolution in the temporal direction. We show results for the chiral transition, vector-axial-vector degeneracy, and heavy quarkonium, and compare them with earlier results with coarser time resolution.

hep-lat↗

arXiv2025

Combining complex Langevin dynamics with score-based and energy-based diffusion models

Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by this complex Langevin process is not known a priori and notoriously hard to understand. In generative AI, diffusion models can learn distributions, or their log derivatives, from data. We explore the ability of diffusion models to learn the distributions sampled by a complex Langevin process, comparing score-based and energy-based diffusion models, and speculate about possible applications.

hep-lat↗

arXiv2025

Phase diagram and eigenvalue dynamics of stochastic gradient descent in multilayer neural networks

Hyperparameter tuning is one of the essential steps to guarantee the convergence of machine learning models. We argue that intuition about the optimal choice of hyperparameters for stochastic gradient descent can be obtained by studying a neural network's phase diagram, in which each phase is characterised by distinctive dynamics of the singular values of weight matrices. Taking inspiration from disordered systems, we start from the observation that the loss landscape of a multilayer neural network with mean squared error can be interpreted as a disordered system in feature space, where the learnt features are mapped to soft spin degrees of freedom, the initial variance of the weight matrices is interpreted as the strength of the disorder, and temperature is given by the ratio of the learning rate and the batch size. As the model is trained, three phases can be identified, in which the dynamics of weight matrices is qualitatively different. Employing a Langevin equation for stochastic gradient descent, previously derived using Dyson Brownian motion, we demonstrate that the three dynamical regimes can be classified effectively, providing practical guidance for the choice of hyperparameters of the optimiser.

cond-mat.dis-nn↗

arXiv2025

Finite temperature hadronic spectral properties

The FASTSUM collaboration has a long-standing project examining hadronic properties using anisotropic lattice QCD. We determine the spectral properties of bottomonia at finite temperature using lattice NRQCD and describe how our newer simulations improve our control over systematic errors. Motivated by these efforts, the temperature dependence of charm hadron masses is determined where it is found that temperature effects can extend into the confining phase and that some species remain stable deep past the pseudo-critical temperature.

hep-lat↗

arXiv2025

Spectral properties of bottomonium at high temperature: a systematic investigation

We investigate spectral features of bottomonium at high temperature, in particular the thermal mass shift and width of ground state S-wave and P-wave state. We employ and compare a range of methods for determining these features from lattice NRQCD correlators, including direct correlator analyses (multi-exponential fits and moments of spectral functions), linear methods (Backus-Gilbert, Tikhonov and HLT methods), and Bayesian methods for spectral function reconstruction (MEM and BR). We comment on the reliability and limitations of the various methods.

hep-lat↗

arXiv2025

Strategic White Paper on AI Infrastructure for Particle, Nuclear, and Astroparticle Physics: Insights from JENA and EuCAIF

Artificial intelligence (AI) is transforming scientific research, with deep learning methods playing a central role in data analysis, simulations, and signal detection across particle, nuclear, and astroparticle physics. Within the JENA communities-ECFA, NuPECC, and APPEC-and as part of the EuCAIF initiative, AI integration is advancing steadily. However, broader adoption remains constrained by challenges such as limited computational resources, a lack of expertise, and difficulties in transitioning from research and development (R&D) to production. This white paper provides a strategic roadmap, informed by a community survey, to address these barriers. It outlines critical infrastructure requirements, prioritizes training initiatives, and proposes funding strategies to scale AI capabilities across fundamental physics over the next five years.

astro-ph.IM↗

arXiv2025

Physics-Conditioned Diffusion Models for Lattice Gauge Theory

We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in two spacetime dimensions and find that a model trained at a small inverse coupling constant can be extrapolated to larger inverse coupling regions without encountering the topological freezing problem. Additionally, the trained model can be employed to sample configurations on different lattice sizes without requiring further training. The exactness of the generated samples is ensured by incorporating Metropolis-adjusted Langevin dynamics into the generation process. Furthermore, we demonstrate that this approach enables more efficient sampling of topological quantities compared to traditional algorithms such as Hybrid Monte Carlo and Langevin simulations.

hep-lat↗

arXiv2025

NRQCD Bottomonium at non-zero temperature using time-derivative moments

A well-known challenge for the lattice community is calculating the spectral function from the Euclidean correlator. We have approximated the spectral function and derived the mass and thermal width of particles through the time derivatives of the lattice correlator moments. We have focused on extracting the properties of bottomonium states, specifically $\Upsilon$ and $\chi_{b1}$. We will give an overview of the time-derivative moments approach and present results for the temperature dependence of the mass and width of both bottomonium states. The zero temperature results are consistent with experimental values, while results at higher temperatures are similar to those obtained using other methods.

hep-lat↗

arXiv2025

The NRQCD $\Upsilon$ spectrum at non-zero temperature using Backus-Gilbert regularisations

Understanding how the properties of heavy mesons change as temperature increases is crucial for gaining valuable insights into the quark-gluon plasma. Information about meson masses and decay widths is encoded in the meson spectral function, which, in principle, can be extracted from Euclidean correlation functions via generalised Laplace transformations. However, this inverse problem is ill-posed for lattice correlation functions and requires regularisation. In this work, we present the latest results for bottomonium spectral functions obtained within the lattice NRQCD framework using the Backus-Gilbert regularisation, along with two other variants, one of which is commonly referred to as the HLT method. Our analysis employs Generation 2L anisotropic lattice configurations produced by the \textsc{Fastsum} collaboration.

hep-lat↗