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

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.