Epsilon-expansion in the N-component phi(4) model

摘要

The formalism of projection Hamiltonians is applied to the N-component O(N)-invariant phi(4) model in the Euclidean and p-adic spaces. We use two versions of the E-expansion (with epsilon = 4 - d and with epsilon = alpha - 3d/2, where alpha is the renormalization group parameter) and evaluate the critical indices v and 71 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 nou-Gaussian fixed point of the renormalization group.