The model is a linear chain in which each spin interacts with its 2r nearest neighbors, the interaction energy being proportional to 1/r. Using a method similar to that of Montroll, the partition function of the model in the thermodynamic limit is shown to be related to the largest eigenvalue of a certain matrix. The largest eigenvalue of the matrix is determined numerically for 3 < r < 12.
Also, a correct method is demonstrated for evaluating an improper limit of the model, in which the interaction range is set to the chain length before the limit of an infinite number of spins is taken. Previously published works have performed this calculation incorrectly.
Although the numerical results show some evidence of convergence to the improper limit, the results are inconclusive and furthermore raise doubts about the practicality of the numerical method in this context.
| Identifer | oai:union.ndltd.org:WKU/oai:digitalcommons.wku.edu:theses-3421 |
| Date | 01 January 1981 |
| Creators | Green, Jimmy |
| Publisher | TopSCHOLAR® |
| Source Sets | Western Kentucky University Theses |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Masters Theses & Specialist Projects |
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