The 〈A2〉 asymmetry and longitudinal propagator in lattice SU(2) gluodynamics at T ≃ Tc

Abstract

We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two gluon condensate as well as the longitudinal gluon propagator at T Tc in the Landau-gauge SU (2) lattice gauge theory. We show that substantial correlation between the asymmetry and the Polyakov loop as well as the correlation between the longitudinal propagator and the Polyakov loop pave the way to studies of the critical behavior of the asymmetry and the longitudinal propagator. The respective values of critical exponents and amplitudes are evaluated.

⟨A2⟩ asymmetry in lattice SU(2) gluodynamics at Bornyakov1, Mitrjushkin2 2019Phys. Rev. D

“…a neighborhood of the point τ = 0 associated with the deconfinement transition: say, A 0 changes by some 5% as τ changes from −0.1 to 0.0 . In the SU (2) case, they not only posses this property but also depend very weakly on the lattice volume [9]. For this reason, it is natural to assume that the lattice size ∼ 2 fm used in our study is sufficiently large for their evaluation.…”

“…We suggested a new approach to the studies of the longitudinal propagator at zero momentum D L (0), which makes it possible to clarify its critical behavior in the infinite-volume limit of the SU (2) gluodynamics and evaluate the respective critical exponent to 6-digit precision [9]. It was shown that the critical exponent γ is unrelated to the critical behavior of D L (0).…”

Correlations and Critical Behavior in Lattice Gluodynamics

“…Nevertheless, our conclusion of the critical behavior of the propagator presenrted in Refs. [9][10][11] holds true because it is based on the assumption of the smooth dependence of the conditional average hD(⌧)i P on P, no assumptions on its variance are made. Therewith, the regression curve can be extracted from the data only with a limited precision, therefore, the concept of smoothness should be formulated for the corridor of errors rather than for the proper function.…”

“…Recently, it was demonstrated that correlations between the Polyakov loop and the zeromomentum longitudinal propagator considerably facilitate the analysis of its critical behavior both in the SU(2) [9,10] and SU(3) [11] gluodynamics. This made it possible to describe critical behavior of the asymmetry and the propagator with unprecendented precision.…”

Correlations and Critical Behavior in Lattice Gluodynamics

“…Recently, it was demonstrated that correlations between the Polyakov loop and the zeromomentum longitudinal propagator considerably facilitate the analysis of its critical behavior both in the SU(2) [9,10] and SU(3) [11] gluodynamics. This made it possible to describe critical behavior of the asymmetry and the propagator with unprecendented precision.…”