Universality hypothesis breakdown at one-loop order

Abstract

We probe the universality hypothesis by analytically computing the at least two-loop corrections to the critical exponents for q-deformed OðNÞ self-interacting λϕ 4 scalar field theories through six distinct and independent field-theoretic renormalization group methods and ϵ-expansion techniques. We show that the effect of q deformation on the one-loop corrections to the q-deformed critical exponents is null, so the universality hypothesis is broken down at this loop order. Such an effect emerges only at the two-loop and higher levels, and the validity of the universality hypothesis is restored. The q-deformed critical exponents obtained through the six methods are the same and, furthermore, reduce to their nondeformed values in the appropriated limit.

Influence of exact Lorentz-violating mechanism on the critical exponents for massive q-deformed λϕ4 scalar field theory

“…Once again, the relations η q ≡ γ φ,q (u * ) and ν −1 q ≡ 2 − η q − γ φ 2 ,q (u * ) when applied by using the Lorentz-violating q-deformed nontrivial fixed point aforementioned we obtain the Lorentz-invariant q-deformed critical exponents [10]. This completes our proposed task and shows that the q-deformed critical exponents besides being universal quantities since are the same in the three distinct and independent methods are insensible to the Lorentz-violating symmetry breaking mechanism.…”

“…It was shown early that this factor arises in calculations of quantum corrections in superfield supersymmetric aetherlike Lorentz-breaking models [47]. If we compute the two independent Lorentz-violating q-deformed critical exponents through the two relations η q ≡ γ φ,q (u * ) and ν −1 q ≡ 2 − γ m 2 ,q (u * ) and the remaining four ones through the four scaling relations [8], we obtain the corresponding Lorentz-invariant q-deformed ones [10], at least at the next-toleading order considered here. We now proceed to evaluate Lorentz-violating q-deformed critical exponents in the next two remaining methods.…”

“…The integral I is a number that can be evaluated analytically in terms of the dilogarithm function of certain argument [49]. Now by applying the relations η q ≡ γ φ,q (u * ) and ν −1 q ≡ 2 − η q − γ φ 2 ,q (u * ), the integral I is is canceled out in the middle of computations and we obtain that the Lorentz-violating q-deformed critical exponents are the same as their Lorentz-invariant counterparts [10].…”

“…Recently, the radiative quantum corrections to critical exponents for q-deformed O(N) λφ 4 scalar field theories were evaluated , at least, at next-to-leading order [10]. This theory is a CPT-even aether-like scalar field theory [11][12][13], for which previous results were obtained as its insertion in the Lorentz-violating extension of the standard model, dispersion relations, aether compactification, the one-loop effective potential corresponding to the action of the scalar field etc.…”

Effective spin-2 quasi-particles at linear dispersive five-fold degenerate points with tunable topological Chern numbers

“…These have distinct topological properties [32][33][34]. In addition to the works mentioned above, spin-1 can also be realized in condensed matter systems [35][36][37][38][39], quantum systems [40][41][42], and cold atom or lattice models [43][44][45][46][47][48][49]. As for spin-3/2, the massive relativistic spin-3/2 quasiparticle has been realized in condensed matter systems [50].…”