Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D_PQ
| Autor: | Baxter, R. J. |
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| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | J. Phys. A Math. Theor. 43, 145002 (16 pages) (2010) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8113/43/14/145002 |
| Popis: | For the Ising model, the calculation of the spontaneous magnetization leads to the problem of evaluating a determinant. Yang did this by calculating the eigenvalues in the large-lattice limit. Montroll, Potts and Ward expressed it as a Toeplitz determinant and used Szego's theorem: this is almost certainly the route originally travelled by Onsager. For the corresponding problem in the superintegrable chiral Potts model, neither approach appears to work: here we show that the determinant D_PQ can be expressed as that of a product of two Cauchy-like matrices. One can then use the elementary exact formula for the Cauchy determinant. One of course regains the known result, originally conjectured in 1989. Comment: 16 pages, no figures; revised 11 Jan 2010 to correct citations and to include reference to subsequent work |
| Databáze: | arXiv |
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