726 research outputs found

### Lifting the Gribov ambiguity in Yang-Mills theories

We propose a new one-parameter family of Landau gauges for Yang-Mills
theories which can be formulated by means of functional integral methods and
are thus well suited for analytic calculations, but which are free of Gribov
ambiguities and avoid the Neuberger zero problem of the standard Faddeev-Popov
construction. The resulting gauge-fixed theory is perturbatively renormalizable
in four dimensions and, for what concerns the calculation of ghost and gauge
field correlators, it reduces to a massive extension of the Faddeev-Popov
action. We study the renormalization group flow of this theory at one-loop and
show that it has no Landau pole in the infrared for some - including physically
relevant - range of values of the renormalized parameters.Comment: 8 pages, 1 figure; published version (PLB), minor corrections,
references adde

### An exact renormalization group approach to frustrated magnets

Frustrated magnets are a notorious example where usual perturbative methods
fail. Having recourse to an exact renormalization group approach, one gets a
coherent picture of the physics of Heisenberg frustrated magnets everywhere
between d=2 and d=4: all known perturbative results are recovered in a single
framework, their apparent conflict is explained while the description of the
phase transition in d=3 is found to be in good agreement with the experimental
context.Comment: 4 pages, Latex, invited talk at the Second Conference on the Exact
Renormalization Group, Rome, September 2000, for technical details see
http://www.lpthe.jussieu.fr/~tissie

### Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond

We study the confinement-deconfinement phase transition of pure Yang-Mills
theories at finite temperature using a simple massive extension of standard
background field methods. We generalize our recent next-to-leading-order
perturbative calculation of the Polyakov loop and of the related background
field effective potential for the SU(2) theory to any compact and connex Lie
group with a simple Lie algebra. We discuss in detail the SU(3) theory, where
the two-loop corrections yield improved values for the first-order transition
temperature as compared to the one-loop result. We also show that certain
one-loop artifacts of thermodynamical observables disappear at two-loop order,
as was already the case for the SU(2) theory. In particular, the entropy and
the pressure are positive for all temperatures. Finally, we discuss the groups
SU(4) and Sp(2) which shed interesting light, respectively, on the relation
between the (de)confinement of static matter sources in the various
representations of the gauge group and on the use of the background field
itself as an order parameter for confinement. In both cases, we obtain
first-order transitions, in agreement with lattice simulations and other
continuum approaches.Comment: 35 pages, 20 figure

### Deconfinement transition in SU(N) theories from perturbation theory

We consider a simple massive extension of the Landau-DeWitt gauge for SU($N$)
Yang-Mills theory. We compute the corresponding one-loop effective potential
for a temporal background gluon field at finite temperature. At this order the
background field is simply related to the Polyakov loop, the order parameter of
the deconfinement transition. Our perturbative calculation correctly describes
a quark confining phase at low temperature and a phase transition of second
order for $N=2$ and weakly first order for $N=3$. Our estimates for the
transition temperatures are in qualitative agreement with values from lattice
simulations or from other continuum approaches. Finally, we discuss the
effective gluon mass parameter in relation to the Gribov ambiguities of the
Landau-DeWitt gauge.Comment: 10 pages, 3 figure

### 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

### Yang-Mills correlators at finite temperature: A perturbative perspective

We consider the two-point correlators of Yang-Mills theories at finite
temperature in the Landau gauge. We employ a model for the corresponding
Yang-Mills correlators based on the inclusion of an effective mass term for
gluons. The latter is expected to have its origin in the existence of Gribov
copies. One-loop calculations at zero temperature have been shown to agree
remarkably well with the corresponding lattice data. We extend on this and
perform a one-loop calculation of the Matsubara gluon and ghost two-point
correlators at finite temperature. We show that, as in the vacuum, an effective
gluon mass accurately captures the dominant infrared physics for the magnetic
gluon and ghost propagators. It also reproduces the gross qualitative features
of the electric gluon propagator. In particular, we find a slight nonmonotonous
behavior of the Debye mass as a function of temperature, however not as
pronounced as in existing lattice results. A more quantitative description of
the electric sector near the deconfinement phase transition certainly requires
another physical ingredient sensitive to the order parameter of the transition.Comment: 16 pages, 12 figures ; Published version (PRD

### 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

### Frustrated magnets in three dimensions: a nonperturbative approach

Frustrated magnets exhibit unusual critical behaviors: they display scaling
laws accompanied by nonuniversal critical exponents. This suggests that these
systems generically undergo very weak first order phase transitions. Moreover,
the different perturbative approaches used to investigate them are in conflict
and fail to correctly reproduce their behavior. Using a nonperturbative
approach we explain the mismatch between the different perturbative approaches
and account for the nonuniversal scaling observed.Comment: 7 pages, 1 figure. IOP style files included. To appear in Journal of
Physics: Condensed Matter. Proceedings of the conference HFM 2003, Grenoble,
Franc

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