Epsilon-expansion in the N-component φ4 model

Abstract

The formalism of projection Hamiltonians is applied to the N-component O(N)-invariant φ4 model in the Euclidean and p-adic spaces. We use two versions of the ε-expansion (with ε = 4 - d and with ε = α - 3d/2, where α is the renormalization group parameter) and evaluate the critical indices ν and η 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. © 2006 Springer Science+Business Media, Inc.