Probing the finite temperature phase transition with $N_f=2$ nonperturbatively improved Wilson fermions

The critical temperature and the nature of the QCD finite temperature phase transition are determined for $N_f=2$ dynamical flavors of nonperturbatively improved Wilson fermions. The calculations are performed on large lattices with temporal extents $N_t=12$, 10, and 8, and lattice spacings down to $a=0.075\mathrm{fm}$. We find that the deconfinement and chiral phase transitions take place at the same temperature. Our results are in broad agreement with a second order phase transition in the chiral limit. The critical temperature at the physical quark mass is found to be $T_c=174(3)(6)\mathrm{MeV}$.

Figure 1

The phase diagram of two-flavor QCD. The solid lines indicate a second (bottom) and a first (top) order transition, respectively, while the dashed line denotes the crossover region.

Figure 2

The average plaquette (○) on the ${24}^{3}10$ (top panel) and ${16}^{3}8$ lattices (bottom panel) at $\beta =5.20$, together with the average plaquette at zero temperature from the ${24}^{3}48$ lattice (□). The dashed line indicates the position of ${\kappa }_c$.

Figure 3

The average Polyakov loop on the ${24}^{3}10$ (top panel) and ${32}^{3}12$ (bottom panel) lattices at $\beta =5.20$ and 5.25, respectively. The solid line in the bottom figure denotes the integral of the Gaussian in Fig. 8 (bottom panel).

Figure 4

The Polyakov-loop susceptibility on the ${16}^{3}8$ (top panel), ${24}^{3}10$ (middle panel), and ${32}^{3}12$ (bottom panel) lattices at $\beta =5.20$, 5.20, and 5.25, respectively, together with a Gaussian adaptation.

Figure 5

The lines of critical temperature $T_c(m)$ for $N_t=8$, 10, and 12, together with the critical hopping parameter ${\kappa }_c$ line. The open circles refer to $T_c(m)$ obtained from the chiral susceptibility.

Figure 6

The phase diagram of clover fermions for $N_t=12$.

Figure 7

The chiral susceptibility on the ${16}^{3}8$ (top panel), ${24}^{3}10$ (middle panel), and ${32}^{3}12$ (bottom panel) lattices at $\beta =5.20$, 5.20, and 5.25, respectively, together with a Gaussian.

Figure 8

The correlator $⟨L\sigma {⟩}_c$ on the ${16}^{3}8$ (top panel), ${24}^{3}10$ (middle panel), and ${32}^{3}12$ (bottom panel) lattices at $\beta =5.20$, 5.20, and 5.25, respectively, together with a Gaussian.

Figure 9

The Polyakov-loop susceptibility ${\chi }_L$ ($\times 7$), the chiral susceptibility ${\chi }_{\sigma }$ ($\times 4$), and the correlator $⟨L\sigma {⟩}_c$ on the ${16}^{3}8$ lattice at $\beta =5.20$.

Figure 10

The pseudocritical temperature $T_c(m)$ as a function of pion mass, together with a fit to the power $m_{\pi }^{1.07}$, according to the three-dimensional $O(4)$ model.