Abstract
The gap equation at finite temperature in the top-quark condensate scheme of electroweak symmetry breaking is proven to have the identical form in both the imaginary and real time formalisms of thermal field theory. By means of the gap equation, combined with the basic relation to define the vacuum expectation value of the effective Higgs field, we analyze the dependence on temperature and chemical potential of the dynamical top-quark mass as the order parameter characteristic of symmetry breaking, and obtain the criticality curve for symmetry restoration. We find out that the critical temperature for and the critical chemical potential for When , the top-quark mass near has the leading behavior with an extra factor dependent on temperature and the momentum cutoff . However, it is generally argued that the symmetry restoration at is still a second-order phase transition.
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