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We calculate the critical exponents for Lorentz-violating O($N$)$\lambda\phi^{4}$ scalar field theories by using two independent methods. Inthe first situation we renormalize a massless theory by utilizing normalizationconditions. An identical task is fulfilled in the second case in a massiveversion of the same theory, previously renormalized in the BPHZ method in fourdimensions. We show that although the renormalization constants, the $\beta$and anomalous dimensions acquire Lorentz-violating quantum corrections, theoutcome for the critical exponents in both methods are identical andfurthermore they are equal to their Lorentz-invariant counterparts. Finally wegeneralize the last two results for all loop levels and we provide symmetryarguments for justifying the latter.

Robustness of the O($N$) universality class