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Register a new userEffective SU(2) Polyakov Loop Theories with Heavy Quarks on the Lattice
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We compare SU(2) Polyakov loop models with different effective actions with data from full two-color QCD simulations around and above the critical temperature. We then apply the effective theories at finite temperature and density to extract quantities like Polyakov loop correlators, effective Polyakov loop potentials and baryon density.
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We simulate SU(2) gauge theory at temperatures ranging from slightly below $T_c$ to roughly $2T_c$ for two different values of the gauge coupling. Using a histogram method, we extract the effective potential for the Polyakov loop and for the phases of the eigenvalues of the thermal Wilson loop, in both the fundamental and adjoint representations. We show that the classical potential of the fundamental loop can be parametrized within a simple model which includes a Vandermonde potential and terms linear and quadratic in the Polyakov loop. We discuss how parametrizations for the other cases can be obtained from this model.
Three-quark potentials are studied in great details in the three-dimensional $SU(3)$ pure gauge theory at finite temperature, for the cases of static sources in the fundamental and adjoint representations. For this purpose, the corresponding Polyakov loop model in its simplest version is adopted. The potentials in question, as well as the conventional quark--anti-quark potentials, are calculated numerically both in the confinement and deconfinement phases. Results are compared to available analytical predictions at strong coupling and in the limit of large number of colors $N$. The three-quark potential is tested against the expected $Delta$ and $Y$ laws and the $3q$ string tension entering these laws is compared to the conventional $qbar{q}$ string tension. As a byproduct of this investigation, essential features of the critical behaviour across the deconfinement transition are elucidated.
We apply the liquid droplet model to describe the clustering phenomenon in SU(2) gluodynamics, especially, in the vicinity of the deconfinement phase transition. In particular, we analyze the size distributions of clusters formed by the Polyakov loops of the same sign. Within such an approach this phase transition can be considered as the transition between two types of liquids where one of the liquids (the largest droplet of a certain Polyakov loop sign) experiences a condensation, while the other one (the next to largest droplet of opposite Polyakov loop sign) evaporates. The clusters of smaller sizes form two accompanying gases, and their size distributions are described by the liquid droplet parameterization. By fitting the lattice data we have extracted the value of Fisher exponent $tau =$ 1.806 $pm$ 0.008. Also we found that the temperature dependences of the surface tension of both gaseous clusters are entirely different below and above the phase transition and, hence, they can serve as an order parameter. The critical exponents of the surface tension coefficient in the vicinity of the phase transition are found. Our analysis shows that the temperature dependence of the surface tension coefficient above the critical temperature has a $T^2$ behavior in one gas of clusters and $T^4$ in the other one.
We study genuine finite density effects in QCD-like theories with three-dimensional Polyakov-loop effective theories for heavy quarks. These are derived from the full QCD-like theories by combined strong-coupling and hopping expansions. In particular, we investigate the cold and dense regimes of phase diagrams where we expect to find Bose-Einstein-condensation of diquark baryons or a fermionic first-order liquid-gas transition, depending on the gauge group of the theory. In two-color QCD, for example, we observe evidence of a continuous zero-temperature transition to finite diquark density when the quark chemical potential $mu$ reaches half the diquark mass, i.e. without binding energy. In G$_2$-QCD we observe, in addition to this Silver Blaze onset of diquark density, a second transition in the density towards an exponential increase by roughly $3mu/T$ corresponding to a finite density of G$_2$-nucleons.
The liquid droplet formula is applied to an analysis of the properties of geometrical (anti)clusters formed in SU(2) gluodynamics by the Polyakov loops of the same sign. Using this approach, we explain the phase transition in SU(2) gluodynamics as a transition between two liquids during which one of the liquid droplets (the largest cluster of a certain Polyakov loop sign) experiences a condensation, while the droplet of another liquid (the next to the largest cluster of the opposite sign of Polyakov loop) evaporates. The clusters of smaller sizes form two accompanying gases, which behave oppositely to their liquids. The liquid droplet formula is used to analyze the size distributions of the gaseous (anti)clusters. The fit of these distributions allows us to extract the temperature dependence of surface tension and the value of Fisher topological exponent $tau$ for both kinds of gaseous clusters. It is shown that the surface tension coeficient of gaseous (anti)clusters can serve as an order parameter of the deconfinement phase transition in SU(2) gluodynamics. The Fisher topological exponent $tau$ of clusters and anticlusters is found to have the same value $1.806 pm 0.008$. This value disagrees with the famous Fisher droplet model, but it agrees well with an exactly solvable model of the nuclear liquid-gas phase transition. This finding may evidence for the fact that the SU(2) gluodynamics and this exactly solvable model of nuclear liquid-gas phase transition are in the same universality class.
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