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.Comment: References added, minor typos correcte
