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Hubbard-type models on the hexagonal lattice are of great interest, as they provide realistic descriptions of graphene and other related materials. Hybrid Monte Carlo simulations offer a first-principles approach to study their phase structure. Here, we review the present status of our work in this direction. [ABSTRACT FROM AUTHOR]

Previous research has shown that Artificial Intelligence is capable of distinguishing between authentic paintings by a given artist and human-made forgeries with remarkable accuracy, provided sufficient training. However, with the limited amount of existing known forgeries, augmentation methods for forgery detection are highly desirable. In this work, we examine the potential of incorporating synthetic artworks into training datasets to enhance the performance of forgery detection. Our investigation focuses on paintings by Vincent van Gogh, for which we release the first dataset specialized for forgery detection. To reinforce our results, we conduct the same analyses on the artists Amedeo Modigliani and Raphael. We train a classifier to distinguish original artworks from forgeries. For this, we use human-made forgeries and imitations in the style of well-known artists and augment our training sets with images in a similar style generated by Stable Diffusion and StyleGAN. We find that the additional synthetic forgeries consistently improve the detection of human-made forgeries. In addition, we find that, in line with previous research, the inclusion of synthetic forgeries in the training also enables the detection of AI-generated forgeries, especially if created using a similar generator. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the properties of the path integral over reparametrizations (or the boundary value of the Liouville field in string theory). Discretizing the path integral, we apply the Metropolis–Hastings algorithm to numerical simulations of a proper (subordinator) stochastic process and find that typical trajectories are not Brownian but rather have discontinuities of the type of Lévy''s flights. We study a fractal structure of these trajectories and show that their Hausdorff dimension is zero. We confirm thereby previous results on QCD scattering amplitudes by analytical and numerical calculations. We also perform Monte Carlo simulations of the path integral over reparametrization in the effective string ansatz for a circular Wilson loop and discuss their subtleties associated with the discretization of Douglas'' functional. [Copyright &y& Elsevier]

We use first-principles quantum Monte Carlo simulations to study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between hydrogen adatoms attached to a graphene sheet. We find that the pairwise RKKY interactions at distances of a few lattice spacings are strongly affected by interelectron interactions, in particular, the potential barrier between widely separated adatoms and the dimer configuration becomes wider and thus harder to penetrate. We also point out that antiferrromagnetic and charge density wave orderings have very different effects on the RKKY interaction. Finally, we analyze the stability of several regular adatom superlattices with respect to small displacements of a single adatom, distinguishing the cases of adatoms which populate either both or only one sublattice of the graphene lattice. [ABSTRACT FROM AUTHOR]

We report on Hybrid Monte Carlo simulations at finite spin density of the π-band electrons in monolayer graphene with realistic interelectron interactions. Unlike simulations at finite charge-carrier density, these are not affected by a fermion-sign problem. Our results are in qualitative agreement with an interaction-induced warping of the Fermi contours and a reduction of the bandwidth as observed in angle-resolved photoemission spectroscopy experiments on charge-doped graphene systems. Furthermore, we find evidence that the neck-disrupting Lifshitz transition, which occurs when the Fermi level traverses the van Hove singularity (VHS), becomes a true quantum phase transition due to interactions. This is in line with an instability of the VHS toward the formation of ordered electronic phases, which has been predicted by a variety of different theoretical approaches. [ABSTRACT FROM AUTHOR]