By simply applying the Local Potential Approximation (LPA) on the Polchinski's Exact Renormalization Group (ERG) flow equation for single Bosonic and spinless Fermionic fields, and initially considering only the coarse-graining (blocking) aspect of Wilson's Renormalization Group program. Within the LPA limit the Polchinski's ERG flow equation simplifies into a heat differential equation for both Bosonic and Fermionic fields. Solving the differential equations leads to logarithmic interactions (logarithmic vertex function) in both Bosonic and Fermionic fields at their fixed points.
Exact renormalization group equation in presence of rescaling anomaly II - The local potential approximation
Revisiting the local potential approximation of the exact renormalization group equation
Asymptotic Analysis of the Local Potential Approximation to the Wetterich Equation
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