Finite-Temperature Phase Structure of Lattice QCD with Wilson Quark Action

The long-standing issue of the nature of the critical line of lattice QCD with the Wilson quark action at finite-temperatures, defined to be the line of vanishing pion screening mass, and its relation to the line of finite-temperature chiral tansition is examined. Analytical and numerical evidence are presented that the critical line forms a cusp at a finite gauge coupling, and the line of chiral transition runs past the tip of the cusp without touching the critical line. Implications on the continuum limit and the flavor dependence of chiral transition are discussed.