Abstract
This paper presents an alternative statistical way to derive the cluster variation method (CVM) for lattice systems. The formulation is developed for a series of different clusters, each of which is the largest overlap cluster between two clusters of the next larger type. We arrive at the CVM expression of the lattice configuration factor by deriving the number of different ways of distributing clusters of a selected type in the lattice so that they overlap each other at the largest overlap clusters in a physically correct manner. The essential assumption employed is that individual overlapping events are statistically independent of each other. This reveals a new statistical aspect of the CVM: The CVM is based on a Bethe tree of clusters of the selected type.
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REFERENCES
C. Domb, Adv. Phys. 9:149 (1960).
M. E. Fisher, Rep. Prog. Phys. 30:615 (1967).
R. Kikuchi, Phys. Rev. 81:988 (1951).
R. Kikuchi, J. Chem. Phys. 19:1230 (1951).
M. Kurata, R. Kikuchi, and T. Watari, J. Chem. Phys. 21:434 (1953).
H. Hijmans and J. de Boer, Physica 21:471 (1955).
H. Hijmans and J. de Boer, Physica 21:485 (1955).
H. Hijmans and J. de Boer, Physica 21:499 (1955).
J. A. Barker, Proc. Roy. Soc. A 216:45 (1953).
See a recent review: T. Morita, Prog. Theor. Phys. Suppl. 115:27 (1994).
T. Morita, J. Stat. Phys. 59:819 (1990).
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Asada, H. A New Statistical Aspect of the Cluster Variation Method for Lattice Systems. Journal of Statistical Physics 98, 621–637 (2000). https://doi.org/10.1023/A:1018615223074
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DOI: https://doi.org/10.1023/A:1018615223074