Universal sextic effective interaction at criticality

Abstract The renormalization group approach in three dimensions is used to estimate the universal critical value of the dimensionless sextic effective coupling constant for the Ising model. The four-loop expansion for g 6 is calculated and resummed resulting in g 6 ∗ = 1.596 , while the most accurate estimate for g 6 ∗ is argued to be equal to 1.61.