A Study of the Free Energy of the Lenz-Ising Model Using the Cluster Variation Method of Morita
Abstract
The Cluster Variation Method proposed by Morita is shown to yield a development of the entropy into an alternating series when applied to the Lenz- Ising Model. Truncation of this series to its first N terms gives an N-th order variationally based approximation to the exact statistical behavior of this system. The first four orders of this sequence of approximations have been carried out in this work. curious behaviors such as complex Curie temperatures have been observed by others and this work shows that such behavior is due to the alternating sign of the terms in the entropy expansion. The effect is large enough to cause a non-physical global minimum to appear on the boundary of the variation space, which is certainly unphysical. A modification of the Cluster Variation Method is effective in suppressing these undesired effects. The (2n+1) -cluster results are then an improvement over those of the (2n+1)-cluster approximation. The (2n)-cluster results are less affected by spurious minima. Keywords: Statistical mechanics; Ising model; Critical point; Ferromagnetism; Order disorder; Thermodynamics; Probability theory; Minimization; Free energy; Cooperative behavior; Curie temperature; Chaos; Variation methods; Entropy; Phase transitions; Clusters.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 06, 1987
- Accession Number
- ADA186023
Entities
People
- Henning Leidecker
- Joann Harnden
- John J. Condon
Organizations
- United States Naval Research Laboratory