  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. Included in
this O(N) analysis is the full evaluation of the mass operator mixing matrix of
anomalous dimensions at four loops. We show that its eigen-exponents are in
agreement with the mass exponents computed at O(1/N^2) in the non-perturbative
large N expansion.
