Fixed-scale approach to finite-temperature lattice QCD with shifted boundaries

We study the thermodynamics of the SU(3) gauge theory using the fixed-scale approach with shifted boundary conditions. The fixed-scale approach can reduce the numerical cost of the zero-temperature part in the equation of state calculations, while the number of possible temperatures is limited by the integer $N_t$, which represents the temporal lattice extent. The shifted boundary conditions can overcome such a limitation while retaining the advantages of the fixed-scale approach. Therefore, our approach enables the investigation of not only the equation of state in detail but also the calculation of the critical temperature with increased precision even with the fixed-scale approach. We also observe numerically that the boundary conditions suppress the lattice artifact of the equation of state, which has been observed in the noninteracting limit.

Figure 1

Plaquette expectation values plotted as a function of the physical temperature. $T=0$ value is measured on a symmetric ${32}^4$ lattice. The inset shows the same data over an expanded range.

Figure 2

Trace anomaly as a function of temperature. The shifted boundary conditions aid in realizing the various temperature simulations at each $N_t$ at the fixed scale. The “continuum” line shows the data from Ref. [13].

Figure 3

Trace anomaly as a function of temperature. The data are the same as those in Fig. 2, but the temperature scale is magnified in the vicinity of the phase transition.

Figure 4

Difference between our trace anomaly results and the continuum values as a function of temperature. Statistical errors are nearly less than the size of the corresponding symbols.

Figure 5

Plot of plaquette susceptibility as a function of temperature. A susceptibility peak is observed at a temperature of approximately 293 MeV, which value is obtained by a quadratic fit with the data of nine points closest to the peak.