Local potential approximation for the renormalization group flow of fermionic field theories

The second functional derivative of the effective potential of pure fermionic field theories is rewritten in a factorized form which facilitates the evaluation of the renormalisation flow rate of the effective action in the Wetterich equation. It is applied to the Local Potential Approximation in cases, when the effective potential depends on scalar composites built from the fermions. The procedure is demonstrated explicitly on the example of the $N_f$-flavor Gross-Neveu model and the one-flavor chiral Nambu--Jona-Lasinio model.

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