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arXiv · 2103.16224

Five loop renormalization of $\phi^3$ theory with applications to the Lee-Yang edge singularity and percolation theory

M. Borinsky·J. A. Gracey·M. V. Kompaniets·O. Schnetz
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Abstract

We apply the method of graphical functions that was recently extended to six dimensions for scalar theories, to $\phi^3$ theory and compute the $\beta$ function, the wave function anomalous dimension as well as the mass anomalous dimension in the $\overline{\mbox{MS}}$ scheme to five loops. From the results we derive the corresponding renormalization group functions for the Lee-Yang edge singularity problem and percolation theory. After determining the $\varepsilon$ expansions of the respective critical exponents to $\mathcal{O}(\varepsilon^5)$ we apply recent resummation technology to obtain improved exponent estimates in 3, 4 and 5 dimensions. These compare favourably with estimates from fixed dimension numerical techniques and refine the four loop results. To assist with this comparison we collated a substantial amount of data from numerical techniques which are included in tables for each exponent.

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M. Borinsky, J. A. Gracey, M. V. Kompaniets, O. Schnetz. 2021-03-30. Five loop renormalization of $\phi^3$ theory with applications to the Lee-Yang edge singularity and percolation theory. https://doi.org/10.1103/physrevd.103.116024

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