Cubic-term removal in a conserved quartic Landau free energy ($\varphi =\psi -c/(3b)$)

For a scalar Landau free energy $f=a{\varphi }^2/2+b{\varphi }^4/4+c{\varphi }^3/3+d\varphi$ with $b>0$, the shift $\varphi =\psi -c/(3b)$ removes the cubic term. The quadratic coefficient becomes $a^{\prime }=a-c^2/(3b)$ and the linear coefficient becomes $d^{\prime }=d-ac/(3b)+2c^3/(27b^2)$. In a closed binary fluid mixture, the linear term is constant at fixed total composition, leaving the symmetric quartic phase coexistence construction in the shifted variable.