Consistency of Blocking Transformationsinthe Finite - Temperature Renormalization

The nite-temperature renormalization group is formulated via the Wilson-Kadanoo blocking transformation. Momentum modes and the Matsubara frequencies are coupled by constraints from a smearing function which plays the role of an infrared cutoo regulator. Using the scalar 4 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.