An effective lattice theory for Polyakov loops

Dittmann, Leander; Heinzl, Thomas; Wipf, Andreas

doi:10.1088/1126-6708/2004/06/005

Cited by 24 publications

(45 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The enhanced symmetry of the measure yields the following geometrical Schwinger-Dyson equations [15],…”

Section: Inverse Monte-carlo Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Effective actions for theSU(2)confinement-deconfinement phase transition

Heinzl¹,

Kaestner²,

Wipf³

2005

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

We compare different Polyakov loop actions yielding effective descriptions of finite-temperature SU (2) Yang-Mills theory on the lattice. The actions are motivated by a simultaneous strongcoupling and character expansion obeying center symmetry and include both Ising and GinzburgLandau type models. To keep things simple we limit ourselves to nearest-neighbor interactions. Some truncations involving the most relevant characters are studied within a novel mean-field approximation. Using inverse Monte-Carlo techniques based on exact geometrical Schwinger-Dyson equations we determine the effective couplings of the Polyakov loop actions. Monte-Carlo simulations of these actions reveal that the mean-field analysis is a fairly good guide to the physics involved. Our Polyakov loop actions reproduce standard Yang-Mills observables well up to limitations due to the nearest-neighbor approximation.

show abstract

“…The enhanced symmetry of the measure yields the following geometrical Schwinger-Dyson equations [15],…”

Section: Inverse Monte-carlo Methodsmentioning

confidence: 99%

“…Altogether, the overdetermined system (12) consists of N a × N s /2 equations which are solved by least-square methods. For more details the reader is referred to Appendix B and [15].…”

Section: Inverse Monte-carlo Methodsmentioning

confidence: 99%

Effective actions for theSU(2)confinement-deconfinement phase transition

Heinzl¹,

Kaestner²,

Wipf³

2005

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

show abstract

“…While perturbation theory at nonzero temperature is badly behaved, resummed perturbation theory works down to much lower temperatures, to a few times T c , where T c is the critical temperature for deconfinement [20][21][22][23][24]. This suggests that nonperturbative effects dominate the region near T c , which we have termed the semi-QGP [25][26][27][28][29]. In this paper, the fourth in a series [30][31][32], we compute the shear viscosity in a simple approximation for the semi-QGP.…”

Section: Introductionmentioning

confidence: 99%

“…To date, a simple form for the effective Lagrangian for the semi-QGP has not been obtained; this would allow one to compute both the pressure and the renormalized loop from the same effective Lagrangian [37]. Clearly analysis from numerical simulations, especially in effective models, is essential to gaining this understanding [28].…”

Section: Introductionmentioning

confidence: 99%

Small shear viscosity in the semiquark gluon plasma

Hidaka

Pisarski

2010

Phys. Rev. D

View full text Add to dashboard Cite

At nonzero temperature in QCD, about the deconfining phase transition there is a "semi" quark gluon plasma (semi-QGP), where the expectation value of the (renormalized) Polyakov loop is less than one. This can be modeled by a semiclassical expansion about a constant field for the vector potential, A 0 , which is diagonal in color. We compute the shear viscosity in the semi-QGP by using the Boltzmann equation in the presence of this background field. To leading, logarithmic order in weak coupling, the dominant diagrams are given by the usual scattering processes of 2 → 2 particles. For simplicity we also assume that both the number of colors and flavors are large.Near the critical temperature T c , where the expectation value of the Polyakov loop is small, the overall density of colored fields decreases according to their color representation, with the density of quarks vanishes linearly with the loop, and that of gluons, quadratically. This decrease in the overall density dominates changes in the transport cross section. As a result, relative to that in the perturbative QGP, near T c the shear viscosity in the semi-QGP is suppressed by two powers of the Polyakov loop. In a semiclassical expansion, the suppression of colored fields depends only upon which color representation they lie in, and not upon their mass. That light and heavy quarks are suppressed in a common manner may help to explain the behavior of charm quarks at RHIC.

show abstract

“…We have done this successfully for SU (2) gauge theory with inverse Monte Carlo techniques [16,23] and plan to publish our results for SU (3) very soon [24]. For the inverse Monte Carlo simulations to work one needs simple geometric Schwinger Dyson equations for the Polyakov loop dynamics.…”

Section: Resultsmentioning

confidence: 99%

Generalized Potts-Models and their Relevance for Gauge Theories

Wipf¹

2007

SIGMA

View full text Add to dashboard Cite

Abstract. We study the Polyakov loop dynamics originating from finite-temperature YangMills theory. The effective actions contain center-symmetric terms involving powers of the Polyakov loop, each with its own coupling. For a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic and antiferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents ν and γ at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state spin Potts model.

show abstract

An effective lattice theory for Polyakov loops

Cited by 24 publications

References 36 publications

Effective actions for theSU(2)confinement-deconfinement phase transition

Effective actions for theSU(2)confinement-deconfinement phase transition

Small shear viscosity in the semiquark gluon plasma

Generalized Potts-Models and their Relevance for Gauge Theories

Contact Info

Product

Resources

About