We study stability of the SYK4 model with a large but finite number of fermions N with respect to a perturbation, quadratic in fermionic operators. We develop  analytic perturbation theory in the amplitude of the SYK2 perturbation and demonstrate stability of the SYK4
infra-red asymptotic behavior characterized by a Green function G(t) µ 1/t3/2, with respect to weak  perturbation.  This result is supported by exact numerical diagornalization.  Our results open the way to build a theory of non-Fermi-liquid states of strongly interacting fermions.
A. V. Lunkin, K. S. Tikhonov, M. V. Feigel'man     arxiv:1806.11211
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