Finite temperature transition in lattice QCD with the strange quark

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We study the nature of the finite temperature phase transition of Quantum Chromodynamics (QCD) using the lattice formalism, which allows us nonperturbative investigations with supercomputers. We adopt Wilson fermions for quarks.(1) With the standard lattice action, the nature of finite temperature transitions is studied for the cases of 2,3, and 6 flavors of degenerate quarks and also for the case of massless up and down quarks and a light strange quark. Our simulations indicate that the finite temperature transition in the chiral limit is continuous for two flavors, while it is of first order for 3 and 6 flavors. We find that the transition is of first order for the case of massless up and down quarks and the physical strange quark. This result is different from the previous result with staggered quarks. Since the deviation from the continuum limit is large in both studies on present lattices, a calculation with larger lattice or with an improved action would be needed in order to obt … More ain a definite conclusion about the nature of the QCD transition.(2) The finite temperature transition of QCD with two degenerate light quarks is studied with a renormalization group improved gauge action and the Wilson quark action. It is shown that the chiral condensate satisfies remarkably a scaling relation with the exponents of the three dimensional O (4) Heisenberg model. This indicates that the chiral transition in two-flavor QCD is of second order in the continuum limit.(3) We also investigate the zero temperature phase structure of QCD for flavors from 2 up to 300. Based on numerical results we propose the following picture : When N_F <greater than or equal> 17, there is only a trivial fixed point and therefore the theory in the continuum limit is trivial. On the other hand, when 16 <greater than or equal> N_F <greater than or equal> 7, there is a non-trivial fixed point and therefore the theory is non-trivial with anomalous dimensions, however, without quark confinement. Theories which satisfy both quark confinement and spontaneous chiral symmetry breaking in the continuum limit exist only for N_F <less than Less