Finite temperature QCD with two flavors of nonperturbatively improved Wilson fermions

We study QCD with two flavors of nonperturbatively improved Wilson fermions at finite temperature on the ${16}^{3}8$ lattice. We determine the transition temperature at lattice spacing as small as $a\sim 0.12$ fm, and study string breaking below the finite temperature transition. We find that the static potential can be fitted by a two-state ansatz, including a string state and a two-meson state. We investigate the role of Abelian monopoles at finite temperature.

Figure 1

Lines of constant $r_0/a$ (solid lines) and constant $m_{\pi }/m_{\rho }$ (dotted lines) at $T=0$. Crosses indicate points where simulations are done.

Figure 2

Scatter plots of the Polyakov loop in the complex plane for various temperatures.

Figure 3

The expectation value of the non-Abelian Polyakov loop as a function of $\kappa$.

Figure 4

The expectation value of monopole and photon Polyakov loops as functions of $\kappa$.

Figure 5

The expectation value of the Abelian Polyakov loop as a function of $\kappa$. The product of monopole and photon Polyakov loops is also shown.

Figure 6

The non-Abelian Polyakov loop susceptibility as a function of $\kappa$ together with the fit.

Figure 7

The same as in Fig. 6 but for the Abelian, the monopole and the photon Polyakov loop susceptibilities. The Abelian (photon) Polyakov loop susceptibility has been enhanced by a factor of 10 (100).

Figure 8

The transition temperature as a function of $m_{\pi }/m_{\rho }$ from this work (triangle), from [1] (squares), and from [22] (circle).

Figure 9

Effect of hypercubic blocking on the potential at $\beta =5.2$, $\kappa =0.1335$.

Figure 10

The heavy quark potential at $\beta =5.2$ for $T/T_c=0.863$ and $0.979$, together with the fit using $\alpha =0.33$. The horizontal lines show the asymptotic value of the potential, where the shaded area indicates the error.

Figure 11

The string tension from a fit of the two-state ansatz (26) as a function of temperature. The quenched value of the string tension [46] is shown for comparison with the shaded area indicating the error bar. The upper (dashed) curve shows the prediction of the effective string model [47].

Figure 12

The constituent quark mass from a fit of the two-state ansatz (26) as a function of temperature. The dash-dotted line indicates the zero-temperature value of the mass $m_{sl}$.

Figure 13

The string potential and the constituent mass as a function of distance at $\beta =5.2$ for $\kappa =0.1335$ ($T/T_c=0.863$). The shaded regions indicate the errors.

Figure 14

The same as in Fig. 13 but for $\kappa =0.1343$ ($T/T_c=0.979$).

Figure 15

The string breaking distance $r_{sb}$ as a function of temperature. The dash-dotted line indicates the corresponding zero-temperature value [3].

Figure 16

The monopole part of the potential as a function of distance at $\beta =5.2$ for $T/T_c=0.863$ and $0.979$, together with a fit of the form (32) (dashed curve). The horizontal lines show the asymptotic value of the potential, where the shaded area indicates the error.

Figure 17

The string tension of the monopole part of the potential as a function of temperature. The curves are the same as in Fig. 11.

Figure 18

The same as in Fig. 17 but for the constituent quark mass. The dash-dotted line indicates the zero-temperature value of the mass $m_{sl}$.

Figure 19

The string breaking distance $r_{sb}^{\mathrm{mon}}$ obtained from the monopole potential as a function of temperature. The dash-dotted line indicates the corresponding zero-temperature value [3].

Figure 20

The monopole part of the action density (a), the monopole part of the color electric field (b) and the solenoidal monopole current in the plane perpendicular to the flux tube (c) at $T/T_c=0.979$ and distances (from top to bottom) 0.5, 0.8 and $1.3\mathrm{fm}$.

Figure 21

The monopole density as a function of temperature.

Figure 22

The asymmetry of the monopole density as a function of temperature.