| Numéro |
J. Phys. I France
Volume 7, Numéro 2, February 1997
|
|
|---|---|---|
| Page(s) | 255 - 272 | |
| DOI | https://doi.org/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 Kikuchi21 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)
Abstract
The interphase excess free energy
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
based on the boundary profile, the SP approach skips the profile and directly evaluates
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
values are calculated. For the 2-D square lattice, the limit of the SP
for
is very close to the exact value of Onsager for the
orientation and to that of Fisher and Ferdinand for
. 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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