Convergence of the cluster-variation method for a system on a triangular lattice

J. Kevin McCoy, Ryoichi Kikuchi and Hiroshi Sato

Physica A: Statistical Mechanics and its Applications, 1981, vol. 109, issue 3, 445-464

Abstract: The paper studies the convergence of the cluster-variation method to the rigorous result as the cluster size increases. The calculation is done on the phase boundary at T = 0 between the A2B-type ordered phase and the disordered phase on a two-dimensional triangular lattice with nearest-neighbor interaction. It is shown that the phase boundary at (T = 0) is obtained by maximizing the entropy under the constraint that only a limited number of atomic configurations are allowed. Formulations are developed for clusters of n = 3, 5, 7, 9,11, and 13 points. When thermodynamic quantities which are calculated using these clusters are plotted against 1/n, they approach the known rigorous (n = ∞) results more or less linearly but with a pseudo-period of δn = 6. An exception is the square of the long-range order, which bends down as 1/n tends to zero.

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:109:y:1981:i:3:p:445-464

DOI: 10.1016/0378-4371(81)90005-4

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