736 research outputs found
Yang-Mills correlators across the deconfinement phase transition
We compute the finite temperature ghost and gluon propagators of Yang-Mills
theory in the Landau-DeWitt gauge. The background field that enters the
definition of the latter is intimately related with the (gauge-invariant)
Polyakov loop and serves as an equivalent order parameter for the deconfinement
transition. We use an effective gauge-fixed description where the
nonperturbative infrared dynamics of the theory is parametrized by a gluon mass
which, as argued elsewhere, may originate from the Gribov ambiguity. In this
scheme, one can perform consistent perturbative calculations down to infrared
momenta, which have been shown to correctly describe the phase diagram of
Yang-Mills theories in four dimensions as well as the zero-temperature
correlators computed in lattice simulations. In this article, we provide the
one-loop expressions of the finite temperature Landau-DeWitt ghost and gluon
propagators for a large class of gauge groups and present explicit results for
the SU(2) case. These are substantially different from those previously
obtained in the Landau gauge, which corresponds to a vanishing background
field. The nonanalyticity of the order parameter across the transition is
directly imprinted onto the propagators in the various color modes. In the
SU(2) case, this leads, for instance, to a cusp in the electric and magnetic
gluon susceptibilities as well as similar signatures in the ghost sector. We
mention the possibility that such distinctive features of the transition could
be measured in lattice simulations in the background field gauge studied here.Comment: 28 pages, 17 figures; published versio
Infrared propagators of Yang-Mills theory from perturbation theory
We show that the correlation functions of ghosts and gluons for the pure
Yang-Mills theory in Landau gauge can be accurately reproduced for all momenta
by a one-loop calculation. The key point is to use a massive extension of the
Faddeev-Popov action. The agreement with lattice simulation is excellent in
d=4. The one-loop calculation also reproduces all the characteristic features
of the lattice simulations in d=3 and naturally explains the pecularities of
the propagators in d=2.Comment: 4 pages, 4 figures
Critical properties of a continuous family of XY noncollinear magnets
Monte Carlo methods are used to study a family of three dimensional XY
frustrated models interpolating continuously between the stacked triangular
antiferromagnets and a variant of this model for which a local rigidity
constraint is imposed. Our study leads us to conclude that generically weak
first order behavior occurs in this family of models in agreement with a recent
nonperturbative renormalization group description of frustrated magnets.Comment: 5 pages, 3 figures, minor changes, published versio
Gauged supersymmetries in Yang-Mills theory
In this paper we show that Yang-Mills theory in the
Curci-Ferrari-Delbourgo-Jarvis gauge admits some up to now unknown local linear
Ward identities. These identities imply some non-renormalization theorems with
practical simplifications for perturbation theory. We show in particular that
all renormalization factors can be extracted from two-point functions. The Ward
identities are shown to be related to supergauge transformations in the
superfield formalism for Yang-Mills theory. The case of non-zero Curci-Ferrari
mass is also addressed.Comment: 11 pages. Minor changes. Some added reference
A unified picture of ferromagnetism, quasi-long range order and criticality in random field models
By applying the recently developed nonperturbative functional renormalization
group (FRG) approach, we study the interplay between ferromagnetism, quasi-long
range order (QLRO) and criticality in the -dimensional random field O(N)
model in the whole (, ) diagram. Even though the "dimensional reduction"
property breaks down below some critical line, the topology of the phase
diagram is found similar to that of the pure O(N) model, with however no
equivalent of the Kosterlitz-Thouless transition. In addition, we obtain that
QLRO, namely a topologically ordered "Bragg glass" phase, is absent in the
3--dimensional random field XY model. The nonperturbative results are
supplemented by a perturbative FRG analysis to two loops around .Comment: 4 pages, 4 figure
Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models
We study by the perturbative Functional Renormalization Group (FRG) the
Random Field and Random Anisotropy O(N) models near , the lower critical
dimension of ferromagnetism. The long-distance physics is controlled by
zero-temperature fixed points at which the renormalized effective action is
nonanalytic. We obtain the beta functions at 2-loop order, showing that despite
the nonanalytic character of the renormalized effective action, the theory is
perturbatively renormalizable at this order. The physical results obtained at
2-loop level, most notably concerning the breakdown of dimensional reduction at
the critical point and the stability of quasi-long range order in , are
shown to fit into the picture predicted by our recent non-perturbative FRG
approach.Comment: 19 pages, 20 figures. Minor correction
Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance
We reformulate the nonperturbative functional renormalization group for the
random field Ising model in a superfield formalism, extending the
supersymmetric description of the critical behavior of the system first
proposed by Parisi and Sourlas [Phys. Rev. Lett. 43, 744 (1979)]. We show that
the two crucial ingredients for this extension are the introduction of a
weighting factor, which accounts for ground-state dominance when multiple
metastable states are present, and of multiple copies of the original system,
which allows one to access the full functional dependence of the cumulants of
the renormalized disorder and to describe rare events. We then derive exact
renormalization group equations for the flow of the renormalized cumulants
associated with the effective average action.Comment: 28 page
An Infrared Safe perturbative approach to Yang-Mills correlators
We investigate the 2-point correlation functions of Yang-Mills theory in the
Landau gauge by means of a massive extension of the Faddeev-Popov action. This
model is based on some phenomenological arguments and constraints on the
ultraviolet behavior of the theory. We show that the running coupling constant
remains finite at all energy scales (no Landau pole) for and argue that
the relevant parameter of perturbation theory is significantly smaller than 1
at all energies. Perturbative results at low orders are therefore expected to
be satisfactory and we indeed find a very good agreement between 1-loop
correlation functions and the lattice simulations, in 3 and 4 dimensions.
Dimension 2 is shown to play the role of an upper critical dimension, which
explains why the lattice predictions are qualitatively different from those in
higher dimensions.Comment: 16 pages, 7 figures, accepted for publication in PR
Critical thermodynamics of three-dimensional chiral model for N > 3
The critical behavior of the three-dimensional -vector chiral model is
studied for arbitrary . The known six-loop renormalization-group (RG)
expansions are resummed using the Borel transformation combined with the
conformal mapping and Pad\'e approximant techniques. Analyzing the fixed point
location and the structure of RG flows, it is found that two marginal values of
exist which separate domains of continuous chiral phase transitions and where such
transitions are first-order. Our calculations yield and
. For the structure of RG flows is identical to
that given by the and 1/N expansions with the chiral fixed point
being a stable node. For the chiral fixed point turns out to be a
focus having no generic relation to the stable fixed point seen at small
and large . In this domain, containing the physical values and , phase trajectories approach the fixed point in a spiral-like
manner giving rise to unusual crossover regimes which may imitate varying
(scattered) critical exponents seen in numerous physical and computer
experiments.Comment: 12 pages, 3 figure
Competition between fluctuations and disorder in frustrated magnets
We investigate the effects of impurities on the nature of the phase
transition in frustrated magnets, in d=4-epsilon dimensions. For sufficiently
small values of the number of spin components, we find no physically relevant
stable fixed point in the deep perturbative region (epsilon << 1), contrarily
to what is to be expected on very general grounds. This signals the onset of
important physical effects.Comment: 4 pages, 3 figures, published versio
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