Exact Lorentz-violating $q$-deformed O($N$) universality class

We examine the influence of exact Lorentz-violating symmetry mechanism on the radiative quantum corrections to the critical exponents for massless $q$-deformed O($N$) $\lambda\phi^{4}$ scalar field theories. For that, we employ three different and independent field-theoretic renormalization group methods for computing analytically the $q$-deformed critical exponents up to next-to-leading order. Then we generalize the former finite loop level results for any loop order. We show that the Lorentz-violating $q$-deformed critical exponents, obtained through the three methods, turn out to be identical and furthermore the same as their Lorentz-invariant $q$-deformed ones. We argue that this result is in accordance with the universality hypothesis.