121 research outputs found
The case against asymptotic freedom
In this talk I give an overview of the work done during the last 15 years in
collaboration with the late Adrian Patrascioiu. In this work we accumulated
evidence against the commonly accepted view that theories with nonabelian
symmetry -- either two dimensional nonlinear models or four
dimensional Yang-Mills theories -- have the property of asymptotic freedom (AF)
usually ascribed to them.Comment: 18 pages, 2 figure
Status of Complex Langevin
I review the status of the Complex Langevin method, which was invented to
make simulations of models with complex action feasible. I discuss the
mathematical justification of the procedure, as well as its limitations and
open questions. Various pragmatic measures for dealing with the existing
problems are described. Finally I report on the progress in the application of
the method to QCD, with the goal of determining the phase diagram of QCD as a
function of temperature and baryonic chemical potential.Comment: Plenary talk given at Lattice 2017, Granada; 21 pages, 14 figures; a
reference added, some more typos correcte
Positive Representations of a Class of Complex Measures
We study the problem of constructing positive representations of complex
measures. In this paper we consider complex densities on a direct product of
groups and look for representations by probability distributions on the
complexification of those groups. After identifying general necessary and
sufficient conditions we propose several concrete realizations. Finally we
study some of those realizations in examples representing problems in abelian
lattice gauge theories.Comment: 19 pages, 3 figures, minor changes to bring it into agreement with
published versio
New Universality Classes in One--Dimensional --Invariant Spin--Models with an --Parametric Action
An action with parameters, which generalizes the
-model, is considered in one dimension for general . We use asymptotic
expansion techniques to determine where the model becomes critical and show
that for the actions considered there exists a family of hypersurfaces whose
asymptotic behaviour determines a one-parameter family of new universality
classes. They interpolate between the -vector-model-class and the -model-class. Furthermore continuum limits are discussed, including the
exceptional case .Comment: 13 page
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