Five-loop renormalization of φ 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 theory and compute the beta function, the wave function anomalous dimension as well as the mass anomalous dimension in the (MS) over bar 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 epsilon expansions of the respective critical exponents to O(epsilon(5)) we apply recent resummation technology to obtain improved exponent estimates in three, four and five dimensions. These compare favorably 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.

Automated summary

Researchers applied the method of graphical functions extended to six dimensions to scalar theories, calculating the beta function, wave function anomalous dimension, and mass anomalous dimension in the (MS) over bar scheme to five-loops. The corresponding renormalization group functions for the Lee-Yang edge singularity problem and percolation theory were derived from the results. Improved exponent estimates in three, four, and five dimensions were obtained through resummation technology after determining the epsilon expansions of the respective critical exponents to O(epsilon(5)).