Boundary Free Energy in the Lattice Model. I. General Formulation

In order to provide the basis for solving the paradox in the theory of the boundary structure, the general expression for the boundary free energy between two phases is derived by applying the cluster variation method rigorously. The surface free energy nσ for the phase boundary is expressed as $\exp {\mathrm{(-n}}_{\sigma }\mathrm{/kT)=}{\mathrm{h}}^{(\mathrm{II})}·{{g}}^{(\mathrm{I})}$ , where h and g are the row and column vectors used in the eigenvalue formulation of the cooperative problem, and (II) and (I) signify the two phases meeting at the boundary. This expression is the same as the one previously derived by Clayton and Woodbury. In the process of the derivation, the local free energy density is identified which will play the key role in solving the paradox in a subsequent paper. The symmetric boundary, the asymmetric boundary, and the case of long‐range interaction are discussed.