We study the curvature of the chiral transition/crossover line between the low-temperature hadronic phase and the high-temperature quark-gluon-plasma phase at low densities, performing simulations of two-flavor QCD with improved Wilson quarks. After
confirming that the chiral order parameter defined by a Ward-Takahashi identity is consistent with the scaling of the O(4) universality class at zero chemical potential, we extend the scaling analysis to finite chemical potential to determine the curvature of the chiral transition/crossover line at low densities assuming the O(4) universality. To convert the curvature in lattice units to that of the $T_c(mu_B)$ in physical units, we evaluate the lattice scale applying a gradient flow method. We find $kappa=0.0006(1)$ in the chiral limit, which is much smaller than that obtained in (2+1)-flavor QCD with improved staggered quarks.
We study the (2+1)-flavor QCD at nonzero temperatures using nonperturbatively improved Wilson quarks of the physical masses by the fixed scale approach. We perform physical point simulations at finite temperatures with the coupling parameters which w
ere adopted by the PACS-CS Collaboration in their studies using the reweighting technique. Zero temperature values are obtained on the PACS-CS configurations which are open to the public on the ILDG/JLDG. Finite temperature configurations are generated with the RHMC algorithm. The lattice sizes are $32^3 times N_t$ with $N_t=14$, 13, $cdots$, 4 which correspond to $T approx 160$--550 MeV. We present results of some basic observables at these temperatures and the status of our calculation of the equation of state.
The reweighting method is widely used in numerical studies of QCD, in particular, for the cases in which the conventional Monte-Carlo method cannot be applied directly, e.g., finite density QCD. However, the application range of the reweighing method
is restricted due to several problems. One of the most severe problems here is the overlap problem. To solve it, we examine a multipoint reweighting method in which simulations at several simulation points are combined in the data analyses. We systematically study the applicability and limitation of the multipoint reweighting method in two-flavor QCD at zero density. Measuring histograms of physical quantities at a series of simulation points, we apply the multipoint reweighting method to calculate the meson masses as continuous functions of the gauge coupling $beta$ and the hopping parameters $kappa$. We then determine lines of constant physics and beta functions, which are needed in a calculation of the equation of state at finite temperature.
