Phi-four diffuse interface
= Phi-four diffuse interface
{title2=$\phi^4$ interface}
For $F=\int[a\phi^2/2+b\phi^4/4+\kappa|\nabla\phi|^2/2]$ with $a<0<b,\kappa$, the planar coexistence interface is
$$
\phi(x)=\phi_B\tanh\frac{x-x_0}{\xi_0},
\qquad
\phi_B=\sqrt{-a/b},
\qquad
\xi_0=\sqrt{-2\kappa/a}.
$$