Phi-four diffuse interface (${\varphi }^4$ interface)

For $F=\int [a{\varphi }^2/2+b{\varphi }^4/4+\kappa |\nabla \varphi {|}^2/2]$ with $a<0<b,\kappa$, the planar coexistence interface is

The excess free energy per area of the phi-four diffuse interface is