Center clusters in full QCD at finite temperature and background magnetic field

We study the center structure of full dynamical QCD at finite temperatures and nonzero values of the background magnetic field using continuum extrapolated lattice data. We concentrate on two particular observables characterizing center clusters: their fractality and the probability for percolation. For temperatures below and around the transition region, the fractal dimension is found to be significantly smaller than three, leading to a vanishing mean free path inside the cluster structure. This finding might be relevant for center symmetry-based models of heavy-ion collisions. In addition, the percolation probability is employed to define the transition temperature and to map out the QCD phase diagram in the magnetic field-temperature plane.

Figure 1

Histogram of the local Polyakov loop phase below and above the transition temperature and the definition of sector numbers according to Eq. (4).

Figure 2

The radius $R$ of the largest cluster as a function of the cut parameter $f$ for our zero-temperature ensembles with various lattice spacings. The dashed line indicates the prescribed cluster radius $R=0.49\mathrm{fm}$.

Figure 3

The cut parameter as a function of the lattice spacing for various fixed cluster radii.

Figure 4

The fractal dimension as a function of the temperature for three lattice spacings. The zero-temperature cluster radius is fixed to $R=0.49\mathrm{fm}$.

Figure 5

The mean free path as a function of the temperature, for three lattice spacings and a continuum extrapolation.

Figure 6

The percolation probability as a function of the temperature for three different values of the magnetic field. The zero-temperature cluster radius is fixed to $R=0.4\mathrm{fm}$.

Figure 7

The transition temperature, defined according to Eq. (9), as a function of the magnetic field for three different lattice spacings. The zero-temperature cluster radius is fixed to $R=0.45\mathrm{fm}$.

Figure 8

Continuum extrapolated transition temperatures as a function of the magnetic field for different zero-temperature cluster radii $R$. (The last three points on the far right are not continuum extrapolated but were obtained on our $N_t=16$ ensemble.)