Four loop renormalization of phi^3 theory in six dimensions

Understand

We renormalize six dimensional phi^3 theory in the modified minimal subtraction (MSbar) scheme at four loops.

• From the resulting beta-function, anomalous dimension and mass anomalous dimension we compute four loop critical exponents relevant to the Lee-Yang edge singularity and percolation problems.
• Using resummation methods and information on the exponents of the relevant two dimensional conformal field theory we obtain estimates for exponents in dimensions 3, 4 and 5 which are in reasonable agreement with other techniques for these two problems.
• The renormalization group functions for the more general theory with an O(N) symmetry are also computed in order to obtain estimates of exponents at various fixed points in five dimensions.