Fate of the Critical Line and Chiral Transition in Finite-Temperature Lattice QCD with the Wilson Quark Action

Finite-temperature phase structure of lattice QCD with the Wilson quark action is analyzed. We show that the critical line at finite temperatures, defined to be the line of vanishing pion screening mass, turns back toward strong coupling, forming a cusp on the $(\beta ,K)$ plane, and that the line of thermal transition runs past the tip of the cusp without touching the critical line. Previous results are discussed in the light of our findings.