  In this work, we compute analytically the infrared divergences of massless
O($N$) self-interacting scalar field theories with Lorentz violation, which are
exact in the Lorentz-violating $K_{\mu\nu}$ coefficients, for evaluating the
corresponding next-to-leading order critical exponents. For that, we apply
three distinct and independent field-theoretic renormalization group methods.
We find that the outcomes for the critical exponents are the same in the three
methods and, furthermore, are identical to their Lorentz invariant
counterparts. We generalize the results for all loop levels by employing a
general theorem arising from the exact procedure and give the corresponding
physical interpretation.
