We determine the (pseudo)critical lines of QCD with two degenerate staggered fermions at nonzero temperature and quark or isospin density, in the region of imaginary chemical potentials; analytic continuation is then used to prolongate to the region of real chemical potentials. We obtain an accurate determination of the curvatures at zero chemical potential, quantifying the deviation between the case of finite quark and of finite isospin chemical potential. Deviations from a quadratic dependence of the pseudocritical lines on the chemical potential are clearly seen in both cases: we try different extrapolations and, for the case of nonzero isospin chemical potential, confront them with the results of direct Monte~Carlo simulations. Finally we find that, as for the finite quark density case, an imaginary isospin chemical potential can strengthen the transition until turning it into strong first order.

We determine the continuum limit of the curvature of the pseudocritical line of QCD with $n_f=2+1$ staggered fermions at nonzero temperature and quark density. We perform Monte Carlo simulations at imaginary baryon chemical potentials with Highly Improved Staggered Quarks (HISQ), adopting the HISQ/tree action discretization as implemented in the code by the MILC Collaboration. Couplings are adjusted so as to move on a line of constant physics, as determined in Ref. [1], with the strange quark mass $m_s$ fixed at its physical value and a light-to-strange mass ratio $m_l/m_s=1/20$. The chemical potential is set at the same value for the three quark species, ${\mu }_l={\mu }_s\equiv \mu$. We attempt an extrapolation to the continuum using the results on lattices with temporal size up to $L_t=12$. Our estimate for the continuum value of the curvature $\kappa$ at zero baryon density, $\kappa =0.020(4)$, is compared with recent lattice results and with experimental determinations of the freeze-out curve.

We determine the curvature of the (pseudo)critical line of QCD with ${n}_{f}\text{ }=\text{ }2\text{ }+\text{ }1$ staggered fermions at nonzero temperature and quark density by analytic continuation from imaginary chemical potentials. Monte Carlo simulations are performed by adopting the highly improved staggered quarks /tree action discretization, as implemented in the code by the MILC Collaboration, suitably modified to include a nonzero imaginary baryon chemical potential. We work on a line of constant physics, as determined in Ref. [1], adjusting the couplings so as to keep the strange quark mass ${m}_{s}$ fixed at its physical value, with a light to strange mass ratio of ${m}_{l}/{m}_{s}=1/20$. In the present investigation, we set the chemical potential at the same value for the three quark species, ${$\mu${}}_{l}={$\mu${}}_{s}$\equiv${}$\mu${}$. We explore lattices of different spatial extensions, ${16}^{3}\ifmmode\times\else\texttimes\fi{}6$ and ${24}^{3}\ifmmode\times\else\texttimes\fi{}6$, to check for finite size effects, and present results on a ${32}^{3}\ifmmode\times\else\texttimes\fi{}8$ lattice, to check for finite cutoff effects. We discuss our results for the curvature $$\kappa${}$ of the (pseudo)critical line at $$\mu${}=0$, which indicate $$\kappa${}=0.018(4)$, and compare them with previous lattice determinations by alternative methods and with experimental determinations of the freeze-out curve.

The transverse profile of the chromoelectric flux tubes in SU(2) and SU(3) pure gauge theories is analyzed by a simple variational ansatz using a strict analogy with ordinary superconductivity. Our method allows to extract the penetration length and the coherence length of the flux tube.

Within the dual superconductor scenario for the QCD confining vacuum, the chromoelectric field generated by a static $q\overline{q}$ pair can be fitted by a function derived, by dual analogy, from a simple variational model for the magnitude of the normalized order parameter of an isolated Abrikosov vortex. Previous results for the SU(3) vacuum are revisited, but here the transverse chromoelectric field is measured by means of the connected correlator of two Polyakov loops and, in order to reduce noise, the smearing procedure is used instead of cooling. The penetration and coherence lengths of the flux tube are then extracted from the fit and compared with previous results.