Consistency of blocking transformations in the finite-temperature renormalization group

The finite-temperature renormalization group is formulated via the Wilson-Kadanoff blocking transformation. Momentum modes and the Matsubara frequencies are coupled by constraints from a smearing function which plays the role of an infrared cutoff regulator. Using the scalar λφ4 theory as an example, we consider four general types of smearing functions and show that, to zeroth order in the derivative expansion, they yield qualitatively the same temperature dependence of the running constants and the same critical exponents within numerical accuracy. (orig.)