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 ${16}^3\times 4$ lattice. Along the lines of constant physics at $m_{\mathrm{PS}}/m_{\mathrm{V}}=0.65$ 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.

• Received 11 September 2009

DOI:https://doi.org/10.1103/PhysRevD.82.014508