J. Phys. I France
Volume 7, Numéro 2, February 1997
Page(s) 255 - 272
DOI: 10.1051/jp1:1997144
J. Phys. I France 7 (1997) 255-272

Scalar Product Method in Statistical Mechanics of Boundary Tension

Pierre Cenedese1 and Ryoichi Kikuchi2

1  CECM/CNRS, 15 rue G. Urbain, 94407 Vitry-sur-Seine, France
2  Department of Materials Science and Engineering, UCLA, Los Angeles, CA 90095-1595, USA

(Received 27 June 1996, revised 14 October 1996, accepted 25 October 1996)

The interphase excess free energy $\sigma$ due to an interphase boundary (IPB) is calculated in the Ising model using the Scalar Product (SP) method. Different from the "sum" method calculation of $\sigma$ based on the boundary profile, the SP approach skips the profile and directly evaluates $\sigma$ from the equilibrium properties of the homogeneous phases meeting at the boundary. Using a series of Cluster Variation Method (CVM) approximations of the basic cluster size n, a series of $\sigma (n)$ values are calculated. For the 2-D square lattice, the limit of the SP $\sigma (n)$ for $n\rightarrow \infty$ is very close to the exact value of Onsager for the $\langle 10\rangle$ orientation and to that of Fisher and Ferdinand for $\langle 10\rangle$. Similar extrapolation was done for the 3-D simple cubic lattice. The result agrees well with the known Monte Carlo results. Because the SP approach does not calculate the profile, computational time and labor are much less than those of the sum method.

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