Robustness of the O(N) universality class

Departamento de Física, Universidade Federal do Piauí - 64049-550, Teresina, PI, Brazil

Received: 19 July 2014
Accepted: 2 October 2014

Abstract

We calculate the critical exponents for Lorentz-violating O(N) λφ⁴ scalar field theories by using two independent methods. In the first situation we renormalize a massless theory by utilizing normalization conditions. An identical task is fulfilled in the second case in a massive version of the same theory, previously renormalized in the BPHZ method in four dimensions. We show that, although the renormalization constants, the β and anomalous dimensions acquire Lorentz-violating quantum corrections, the outcome for the critical exponents in both methods is identical and furthermore they are equal to their Lorentz-invariant counterparts. Finally we generalize the last two results for all loop levels and we provide symmetry arguments for justifying the latter.