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We consider renormalization of four-fermion operators in the critical QED and$SU(N_c)$ version of Gross--Neveu--Yukawa model in non-integer dimensions.Since the number of mixing operators is infinite, the diagonalization of ananomalous dimension matrix becomes a nontrivial problem. At leading order,construction of eigen-operators is equivalent to solving certain three-termrecurrence relations. We find analytic solutions of these recurrence relationsthat allows to determine the spectrum of anomalous dimensions and study theirproperties.

On operator mixing in fermionic CFTs in non-integer dimensions