Power-law running of the effective gluon mass

The dynamically generated effective gluon mass is known to depend non-trivially on the momentum, decreasing sufficiently fast in the deep ultraviolet, in order for the renormalizability of QCD to be preserved. General arguments based on the analogy with the constituent quark masses, as well as explicit calculations using the operator-product expansion, suggest that the gluon mass falls off as the inverse square of the momentum, relating it to the gauge-invariant gluon condensate of dimension four. In this article we demonstrate that the power-law running of the effective gluon mass is indeed dynamically realized at the level of the non-perturbative Schwinger-Dyson equation. We study a gauge-invariant non-linear integral equation involving the gluon self-energy, and establish the conditions necessary for the existence of infrared finite solutions, described in terms of a momentum-dependent gluon mass. Assuming a simplified form for the gluon propagator, we derive a secondary integral equation that controls the running of the mass in the deep ultraviolet. Depending on the values chosen for certain parameters entering into the Ansatz for the fully-dressed three-gluon vertex, this latter equation yields either logarithmic solutions, familiar from previous linear studies, or a new type of solutions, displaying power-law running. In addition, it furnishes a non-trivial integral constraint, which restricts significantly (but does not determine fully) the running of the mass in the intermediate and infrared regimes. The numerical analysis presented is in complete agreement with the analytic results obtained, showing clearly the appearance of the two types of momentum-dependence, well-separated in the relevant space of parameters. Open issues and future directions are briefly discussed.Comment: 37 pages, 5 figure

The critical exponents of the two-dimensional Ising spin glass revisited: Exact Ground State Calculations and Monte Carlo Simulations

The critical exponents for $T\to0$ of the two-dimensional Ising spin glass model with Gaussian couplings are determined with the help of exact ground states for system sizes up to $L=50$ and by a Monte Carlo study of a pseudo-ferromagnetic order parameter. We obtain: for the stiffness exponent $y(=\theta)=-0.281\pm0.002$, for the magnetic exponent $\delta=1.48 \pm 0.01$ and for the chaos exponent $\zeta=1.05\pm0.05$. From Monte Carlo simulations we get the thermal exponent $\nu=3.6\pm0.2$. The scaling prediction $y=-1/\nu$ is fulfilled within the error bars, whereas there is a disagreement with the relation $y=1-\delta$.Comment: 8 pages RevTeX, 7 eps-figures include

QuantCrit: education, policy, ‘Big Data’ and principles for a critical race theory of statistics

Quantitative research enjoys heightened esteem among policy-makers, media and the general public. Whereas qualitative research is frequently dismissed as subjective and impressionistic, statistics are often assumed to be objective and factual. We argue that these distinctions are wholly false; quantitative data is no less socially constructed than any other form of research material. The first part of the paper presents a conceptual critique of the field with empirical examples that expose and challenge hidden assumptions that frequently encode racist perspectives beneath the façade of supposed quantitative objectivity. The second part of the paper draws on the tenets of Critical Race Theory (CRT) to set out some principles to guide the future use and analysis of quantitative data. These ‘QuantCrit’ ideas concern (1) the centrality of racism as a complex and deeply-rooted aspect of society that is not readily amenable to quantification; (2) numbers are not neutral and should be interrogated for their role in promoting deficit analyses that serve White racial interests; (3) categories are neither ‘natural’ nor given and so the units and forms of analysis must be critically evaluated; (4) voice and insight are vital: data cannot ‘speak for itself’ and critical analyses should be informed by the experiential knowledge of marginalized groups; (5) statistical analyses have no inherent value but can play a role in struggles for social justice

Panel Comparability Et La Base De Donnees Paco

Panel Comparability and the PACO Data Base. The CEPS/INSTEAD has been coordinating the European Commission-financed "Panel Comparability (PACO)" project which Involves national longitudinal surveys carried out in Luxembourg. France. Germany. Great Britain. and the United States. The authors address the numerous methodological problems involved in setting up such a data base which permits the comparative study of panel survey data from different countries. </jats:p