  We compute analytically the all-loop level critical exponents for a massless
thermal Lorentz-violating O($N$) self-interacting $\lambda\phi^{4}$ scalar
field theory. For that, we evaluate, firstly explicitly up to next-to-leading
order and later in a proof by induction up to any loop level, the respective
$\beta$-function and anomalous dimensions in a theory renormalized in the
massless BPHZ method, where a reduced set of Feynman diagrams to be calculated
is needed. We investigate the effect of the Lorentz violation in the outcome
for the critical exponents and present the corresponding mathematical
explanation and physical interpretation.
