Solution
= Solution
Far from a planar interface, the equilibrium profile equals a bulk minimum and contributes the uniform density $f(\phi_B)$. The localized transition layer contributes an additional free energy proportional to its area $A$, because translation invariance makes the excess per unit area independent of position. By the definition of <surface tension> as interfacial excess free energy per area,
$$
\boxed{\sigma A=F[\phi_E]-Vf(\phi_B).}
$$