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Five loop renormalization of $φ^3$ theory with applications to the Lee-Yang edge singularity and percolation theory (2103.16224v2)

Published 30 Mar 2021 in hep-th, cond-mat.dis-nn, cond-mat.stat-mech, and hep-lat

Abstract: We apply the method of graphical functions that was recently extended to six dimensions for scalar theories, to $\phi3$ 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 $\mathcal{O}(\varepsilon5)$ 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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