Nature of Roberge-Weiss transition endpoints for heavy quarks in $N_f=2$ lattice QCD with Wilson fermions

The phase structure of QCD with imaginary chemical potential provides information on the phase diagram of QCD with real chemical potential. With imaginary chemical potential $i{\mu }_I=i\pi T$, previous studies show that the Roberge-Weiss (RW) transition endpoints are triple points at both large and small quark masses, and second order transition points at intermediate quark masses. The triple and second order endpoints are separated by two tricritical ones. We present simulations with $N_f=2$ Wilson fermions to investigate the nature of RW transition endpoints. The simulations are carried out at 8 values of the hopping parameter $\kappa$ ranging from 0.020 to 0.140 on different lattice volumes. The Binder cumulant, susceptibility, and reweighted distribution of the imaginary part of the Polyakov loop are employed to determine the nature of RW transition endpoints. The simulations show that the two tricritical points are within the ranges 0.070–0.080 and 0.120–0.140, respectively.

Figure 1

Scaling behavior of the susceptibility of the imaginary part of the Polyakov loop according to the first order critical index (left panel), and to the 3D Ising critical index (right panel) at $\kappa =0.040$.

Figure 2

Reweighted distribution of the imaginary part of the Polyakov loop at $\kappa =0.040$ at the corresponding endpoint ${\beta }_{RW}$.

Figure 3

Scaling behavior of the susceptibility of the imaginary part of the Polyakov loop according to the first order critical index (left panel), and to the 3D Ising critical index (right panel) at $\kappa =0.080$.

Figure 4

Scaling behavior of the susceptibility of imaginary part of the Polyakov loop according to first order critical index (left panel), and to 3D Ising critical index (right panel) at $\kappa =0.120$.

Figure 5

Binder cumulants as a function of $\beta$ on various spatial volumes intersect at one point (left panels), and as a function of $(\beta -{\beta }_c)L_s^{1/\nu }$ with values of ${\beta }_c$, $\nu$ from Table 3 collapse (right panels).

Figure 6

Reweighted distribution of the imaginary part of the Polyakov loop at $\kappa =0.080,0.120$ at the corresponding endpoints ${\beta }_c$ which are extracted by fitting.

Figure 7

Behavior of the susceptibility of the imaginary part of the Polyakov loop (left panels) and Binder cumulant (right panels) with a different selection of $\beta$ values on $L_s=8$ at $\kappa =0.120$.