Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism

Abstract

We probe the two-scale factor universality hypothesis by evaluating, firstly explicitly and analytically at the one-loop order, the loop quantum corrections to the amplitude ratios for O($N$) $\lambda {\varphi }^4$ scalar field theories with rotation symmetry-breaking in three distinct and independent methods in which the rotation symmetry-breaking mechanism is treated exactly. We show that the rotation symmetry-breaking amplitude ratios turn out to be identical in the three methods and equal to their respective rotation symmetry-breaking ones, although the amplitudes themselves, in general, depend on the method employed and on the rotation symmetry-breaking parameter. At the end, we show that all these results can be generalized, through an inductive process based on a general theorem emerging from the exact calculation, to any loop level and physically interpreted based on symmetry ideas.

arXiv comment17 pages, 3 figures

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Cited by in corpus (2)

• Critical exponents and amplitude ratios of scalar nonextensive $q$-field theories
• Influence of conformal symmetry on the amplitude ratios for O($N$) models