 One-loop critical-mass subtraction

For a scalar quartic interaction $g{\varphi }^4/4!$, the tadpole relation $R=r_{\Lambda }+(g/2)I_D(R)$ can be subtracted at the critical point. When $I_D(0)$ exists, $A(T-T_C)=R[1+(g/2)J_D(R)]$, with $J_D(R)=\int d^{D}p(2\pi {)}^{-D}/[p^2(p^2+R)]$. This integral is finite as $R\to 0$ only above four dimensions and is logarithmic at four. A self-consistent one-loop relation is not an exact interacting critical-exponent formula.