We consider the renormalization of four-fermion operators in the critical QED and SU(N-c) thorn version of the Gross-Neveu-Yukawa model in noninteger dimensions. Since the number of mixing operators is infinite, the diagonalization of an anomalous dimension matrix becomes a nontrivial problem. At leading order, the construction of eigenoperators is equivalent to solving certain three-term recurrence relations. We find analytic solutions of these recurrence relations that allow us to determine the spectrum of anomalous dimensions and study their properties.