Epsilon-expansion in the $N$-component $\varphi^4$ model

The formalism of projection Hamiltonians is applied to the $N$-component $O(N)$-invariant $\varphi^4$ model in the Euclidean and $p$-adic spaces. We use two versions of the $\varepsilon$-expansion (with $\varepsilon=4-d$ and $\varepsilon=\alpha-3d/2$ where $\alpha$ is the renormalization group parameter) and evaluate the critical indices $\nu$ and $\eta$ up to the second order of the perturbation theory. The results for the $(4-d)$-expansion then coincide with the known results obtained via the quantum-field renormalization-group methods. Our calculations give evidence that in dimension three, both expansions describe the same non-Gaussian fixed point of the renormalization group.