Influence of exact Lorentz-violating mechanism on the critical exponents for massive $q$-deformed $\lambda\phi^{4}$ scalar field theory

TL;DR

This paper investigates how an exact Lorentz-violating mechanism affects the critical exponents in a massive $q$-deformed scalar field theory, finding that the exponents remain unaffected, supporting the universality hypothesis.

Contribution

It provides a detailed analysis of Lorentz violation effects on critical exponents using multiple renormalization group methods, extending results to all loop levels.

Findings

Critical exponents are insensitive to Lorentz symmetry breaking.

Results support the universality hypothesis in the presence of Lorentz violation.

Methodology applies to any loop level, generalizing previous finite-order results.

Abstract

We probe the influence of Lorentz-violating mechanism, treated exactly, on the radiative quantum corrections to critical exponents for massive $q$-deformed O($N$) $\lambda\phi^{4}$ scalar field theories. We attain that task by employing three distinct and independent field-theoretic renormalization group methods. Firstly we compute the critical exponents up to the finite next-to-leading order for then generalizing the results for any loop level. We show that the $q$-deformed critical exponents are insensible to the Lorentz symmetry breaking mechanism thus agreeing with the universality hypothesis.