Related papers: Asymptotic Scaling and Monte Carlo Data
There is a growing body of evidence that the running of $\alpha_s$ predicted by perturbation (PT) theory is not correctly describing the accelerator experiments at the highest energies. A natural explanation is provided by the authors' 1992…
The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is…
Predictions for (phi^4)_4 theory from renormalization-group-improved perturbation theory, as formulated by Luescher and Weisz, are compared to published (and some unpublished) data from lattice Monte-Carlo simulations of the 4-dimensional…
Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on…
We discuss a new approach of scalar field theory where the small field contributions are treated perturbatively and the large field configurations (which are responsible for the asymptotic behavior of the perturbative series) are neglected.…
Precision tests of QCD perturbation theory are not readily available from experimental data. The main reasons are systematic uncertainties due to the confinement of quarks and gluons, as well as kinematical constraints which limit the…
Lattice Monte Carlo (MC) simulations and the functional Renormalization Group (RG) are powerful approaches that allow for quantitative studies of non-perturbative phenomena such as bound-state formation, spontaneous symmetry breaking and…
Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative.…
In a recent Letter Albano and Saracco study the dynamic critical behavior of some anisotropic driven lattice gases by Monte Carlo (MC) simulations. In this Comment we point out that the Ans\"atze they use to relate the measured scaling…
The QCD-coupling is a necessary input in the computation of many observables, and the parametric error on input parameters can be a dominant source of uncertainty. The coupling can be extracted by comparing high order perturbative…
In general, perturbative expansions of observables in powers of the coupling constant in quantum field theories are asymptotic series. In many cases it is possible to apply resummation techniques to assign a unique finite value to an…
Perturbative expansions of QCD observables in powers of $\alpha_s$ are believed to be asymptotic and non-Borel summable due to the existence of singularities in the Borel plane (renormalons). This fact is connected with the factorization of…
Critical phenomena and Goldstone mode effects in spin models with O(n) rotational symmetry are considered. Starting with the Goldstone mode singularities in the XY and O(4) models, we briefly review different theoretical concepts as well as…
The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the…
We present a lattice Monte Carlo algorithm based on the one originally proposed by Maggs and Rossetto for simulating electrostatic interactions in inhomogeneous dielectric media. The original algorithm is known to produce attractive…
The standard perturbative weak-coupling expansions in lattice models are asymptotic. The reason for this is hidden in the incorrect interchange of the summation and integration. However, substituting the Gaussian initial approximation of…
We study the $2$-component $\phi^4$ model on the simple cubic lattice in the presence of a cubic, or equivalently, a $\mathbb{D}_4$ invariant perturbation. To this end, we perform Monte Carlo simulations in conjunction with a finite size…
Machine learning models are commonly applied to human brain imaging datasets in an effort to associate function or structure with behaviour, health, or other individual phenotypes. Such models often rely on low-dimensional maps generated by…
The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD -- ghost singularities and…
We devise a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…