Phase Diagram of QCD at Finite Temperatures with Wilson Fermions

Phase diagram of QCD with Wilson fermions for various numbers of flavors $N_F$ is discussed. Our simulations mainly performed on a lattice with the temporal size $N_t =4$ indicate the following: The chiral phase transition is of first order when $3 \le N_F \le 6$, while it is continuous when $N_F=2$. For the realistic case of massless u and d quarks and the strange quark with $m_q = 150$ MeV, the phase transition is first order. The sharp transition in the intermediate mass region for $N_F=2$ at $N_t=4$ observed by the MILC group disappears when an RG improvement is made for the pure gauge action.