Critical Exponents in Fermionic Hierarchical Model

We consider the problem of algebraic computation of the critical exponent $\nu$ in the $2N$-component fermionic Dyson model on a hierarchical lattice without the use of perturbation theory. Analyzing the results in a particular case when $N=2$, we conclude that an algebraic approach in this model gives the same expression for $\nu$ as the approach of functional integration via Feynman diagrams in the $p$-adic $\varphi ^4$-model.