Numerical study of the Roberge-Weiss transition

We study the Roberge-Weiss phase transition numerically. The phase transition is associated with the discontinuities in the quark-number density at specific values of imaginary quark chemical potential. We parametrize the quark-number density ${\rho }_q$ by the polynomial fit function to compute the canonical partition functions. We demonstrate that this approach provides a good framework for analyzing lattice QCD data at finite density and a high temperature. We show numerically that, at high temperature, the Lee-Yang zeros lie on the negative real semiaxis provided that the high-quark-number contributions to the grand canonical partition function are taken into account. These Lee-Yang zeros have nonzero linear density, which signals the Roberge-Weiss phase transition. We demonstrate that this density agrees with the quark-number density discontinuity at the transition line.

Figure 1

$Z_{nN}$ (blue crosses) are compared with $Z_{nA}$ (red line) for $N_s=16$. For $n_q>309$ positive values of $Z_{nN}$ are shown by crosses, whereas for negative $Z_{nN}$ we depict $-Z_{nN}$ using green circles.

Figure 2

The quark-number density computed using $Z_{nA}$ for imaginary chemical potential for three volumes and ${\varrho }_{\max }=8.0$ over a restricted range near ${\theta }_I=\pi /3$.

Figure 3

Relative deviation of the quark-number density computed using $Z_{nA}$ for the imaginary chemical potential (left panel) and the real chemical potential (right panel).

Figure 4

LYZ distribution in the fugacity plane. See explanation in the text.

Figure 5

Left: lhs and rhs (for $N_s=16$, 20, 40) of Eq. (24) vs ${\theta }_R$ at ${\theta }_I=\pi /3$. Right: $N_s$ dependence of the distance between the point ${\xi }_B=-1$ and the nearest LYZ.