Phase Transition within a Phase Boundary

The excess free energy σ due to the phase boundary has been expressed previously using the bulk properties of the two phases meeting at the boundary as $$\exp \mathrm{(-A\sigma /kT)=}{\displaystyle \sum _{\nu }}{\mathrm{[p}}^{(\mathrm{II})}{\mathrm{(\nu )p}}^{(\mathrm{I})}{\mathrm{(\nu )]}}^{\text{1/2}},$$ where σ is per unit area, A is the cross‐sectional area of the boundary, and p^(I)(v) is the probability that a configuration v of the lattice plane parallel to the boundary appears in the bulk phase I. The summation goes over all possible configurations of the plane. The present paper applies the above formula to boundaries in the three‐dimensional Ising model using the pair approximation. It is shown that an order‐disorder transition occurs in σ. The ordered state is identified with the interstitial center boundary calculated before.