Equation of state and heavy-quark free energy at finite temperature and density in two flavor lattice QCD with Wilson quark action

We study the equation of state at finite temperature and density in two-flavor QCD with the renormalization group improved gluon action and the clover-improved Wilson quark action on a 16(3) X 4 lattice. Along the lines of constant physics at m(PS)/m(V) = 0.65 and 0.80, we compute the second and forth derivatives of the grand canonical partition function with respect to the quark chemical potential mu(q) = (mu(u) + mu(d))/2 and the isospin chemical potential mu(I) = (mu(u) - mu(d))/2 at vanishing chemical potentials, and study the behaviors of thermodynamic quantities at finite mu(q) using these derivatives for the case mu(I) = 0. In particular, we study density fluctuations at nonezero temperature and density by calculating the quark number and isospin susceptibilities and their derivatives with respect to mu(q). To suppress statistical fluctuations, we also examine new techniques applicable at low densities. We find a large enhancement in the fluctuation of the quark number when the density increased near the pseudocritical temperature, suggesting a critical point at finite mu(q) terminating the first order transition line between hadronic and quark-gluon-plasma phases. This result agrees with the previous results using staggered-type quark actions qualitatively. Furthermore, we study heavy-quark free energies and Debye screening masses at finite density by measuring the first and second derivatives of these quantities for various color channels of heavy quark-quark and quark-antiquark pairs. The results suggest that, to the leading order of mu(q), the interaction between two quarks becomes stronger at finite densities, while that between quark and antiquark becomes weaker.