Chiral phase transition at high temperature in the QCD-like gauge theory

The chiral phase transition at high temperature is investigated using the effect ive potential in the framework of the QCD-like gauge theory with a variational a pproach. We have a second order phase transition at $T_c=136$MeV. We also investigate numerically the temperature dependence of condensate, $f_{\pi }$ a nd $a_2(T)$(coefficient of the quadratic term in the effective potential) and es timate the critical exponents of these quantities.