Lattice QCD at finite temperature and density

We study the phase structure of QCD at finite temperature and density by numerical simulations on a lattice. The most important point for the numerical study at finite density is treatment of the sign problem. We propose a method to avoid the sign problem, which is based on a cumulant expansion of the complex phase in the density of state method combined with the reweighting method. Using the method, we study the critical point terminating a first order phase transition line in lattice QCD at high temperature and density.