Addendum to Wilson's theory of critical phenomena and Callan-Symanzik equations in4−εdimensions

In a previous work, it was shown how to derive the scaling laws near a critical point using renormalized perturbation theory. The calculations of the Callan-Symanzik functions $\beta$ and $\gamma$ which lead to the critical exponents are extended to next order in $\epsilon$. The existence of a solution to the eigenvalue conditions $\beta \mathrm{}\left(g\right)=0\mathrm{}$ in four dimensions, at fourth order in the coupling constant, is shown to be renormalization-dependent.