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In this work we evaluate analytically the ultraviolet divergences ofLorentz-violating massive O($N$) $\lambda\phi^{4}$ scalar field theories, whichare exact in the Lorentz-violating mechanism, firstly explicitly atnext-to-leading order and latter at any loop level through an inductionprocedure based on a theorem following from the exact approach, for computingthe corresponding critical exponents. For attaining that goal, we employ threedifferent and independent field-theoretic renormalization group methods. Theresults found for the critical exponents show that they are identical in thethree distinct methods and equal to their Lorentz invariant counterparts.Furthermore, we show that the results obtained here, based on the singleconcept of loop order of the referred terms of the corresponding$\beta$-function and anomalous dimensions, reduce to the ones obtained throughthe earlier non-exact approach based on a joint redefinition of the field andcoupling constant of the theory, in the appropriate limit.

Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories