Vanishing Beta Function curves from the Functional Renormalisation Group

P. Mati

doi:10.1103/physrevd.91.125038

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arXiv · 1501.00211

Vanishing Beta Function curves from the Functional Renormalisation Group

P. Mati

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Abstract

In this paper we will discuss the derivation of the so-called vanishing beta function curves which can be used to explore the fixed point structure of the theory under consideration. This can be applied to the O($N$) symmetric theories, essentially, for arbitrary dimensions ($D$) and field component ($N$). We will show the restoration of the Mermin-Wagner theorem for theories defined in $D\leq2$ and the presence of the Wilson-Fisher fixed point in $2 4$. Interestingly, one needs to make an excursion to the complex plane to see the triviality of the four-dimensional O($N$) theories. The large-$N$ analysis shows a new fixed point candidate in $4 4$?" [Phys. Rev. D 90, 107702 (2014)].

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P. Mati. 2014-12-31. Vanishing Beta Function curves from the Functional Renormalisation Group. https://doi.org/10.1103/physrevd.91.125038

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