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arXiv · 1502.01289

Robustness of the O($N$) universality class

William C. Vieira·Paulo R. S. Carvalho
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Abstract

We calculate the critical exponents for Lorentz-violating O($N$) $λϕ^{4}$ scalar field theories by using two independent methods. In the first situation we renormalize a massless theory by utilizing normalization conditions. An identical task is fulfilled in the second case in a massive version of the same theory, previously renormalized in the BPHZ method in four dimensions. We show that although the renormalization constants, the $β$ and anomalous dimensions acquire Lorentz-violating quantum corrections, the outcome for the critical exponents in both methods are identical and furthermore they are equal to their Lorentz-invariant counterparts. Finally we generalize the last two results for all loop levels and we provide symmetry arguments for justifying the latter.

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William C. Vieira, Paulo R. S. Carvalho. 2015-02-04. Robustness of the O($N$) universality class. https://doi.org/10.1209/0295-5075%2F108%2F21001

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