The Thermal Renormalization Group for Fermions, Universality, and the Chiral Phase-Transition
We formulate the thermal renormalization group, an implementation of the Wilsonian RG in the real-time (CTP) formulation of finite temperature field theory, for fermionic fields. Using a model with scalar and fermionic degrees of freedom which should describe the two-flavor chiral phase-transition, we discuss the mechanism behind fermion decoupling and universality at second order transitions. It turns out that an effective mass-like term in the fermion propagator which is due to thermal fluctuations and does not break chiral symmetry is necessary for fermion decoupling to work. This situation is in contrast to the high-temperature limit, where the dominance of scalar over fermionic degrees of freedom is due to the different behavior of the distribution functions. The mass-like contribution is the leading thermal effect in the fermionic sector and is missed if a derivative expansion of the fermionic propagator is performed. We also discuss results on the phase-transition of the model considered where we find good agreement with results from other methods.