ε-Expansion Solution of Wilson's Incomplete-Integration Renormalization-Group Equations

Wilson's incomplete-integration renormalization-group equations have been solved in $4-\epsilon$ dimensions for an arbitrary cutoff function. The two relevent exponents are computed to order $\epsilon$ and the exponent $\eta$ is computed to order ${\epsilon }^2$. To order $\epsilon$ the exponents agree with the sharp-cutoff renormalization group. In order ${\epsilon }^2$, however, $\eta$ appears to depend on the choice of the cutoff function.