Universality hypothesis breakdown at one-loop order

TL;DR

This paper investigates the impact of q-deformation on the universality hypothesis in scalar field theories, revealing that universality breaks down at one-loop order but is restored at two-loop order, with consistent results across six methods.

Contribution

The study provides the first analytical computation of two-loop corrections to critical exponents in q-deformed theories using six independent renormalization group methods.

Findings

q-deformation does not affect one-loop critical exponents

Universality breaks down at one-loop order due to q-deformation

Universality is restored at two-loop order with consistent exponents across methods

Abstract

We probe the universality hypothesis by analytically computing, at least, the two-loop corrections to the critical exponents for $q$-deformed O($N$) self-interacting $\lambda\phi^{4}$ scalar field theories through six distinct and independent field-theoretic renormalization group methods and $\epsilon$-expansion techniques. We show that the effect of $q$-deformation on the one-loop corrections to the $q$-deformed critical exponents is null, so universality hypothesis is broken down at this loop order. Such effect emerges just, at least, at two-loop level and the validity of universality hypothesis is restored. The $q$-deformed critical exponents obtained through the six methods are the same and, furthermore, reduce to their non-deformed values in the appropriated limit.