# Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D PQ - Condensed Matter > Statistical Mechanics

Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D PQ - Condensed Matter > Statistical Mechanics - Download this document for free, or read online. Document in PDF available to download.

Abstract: For the Ising model, the calculation of the spontaneous magnetization leadsto the problem of evaluating a determinant. Yang did this by calculating theeigenvalues in the large-lattice limit. Montroll, Potts and Ward expressed itas a Toeplitz determinant and used Szego-s theorem: this is almost certainlythe route originally travelled by Onsager. For the corresponding problem in thesuperintegrable chiral Potts model, neither approach appears to work: here weshow that the determinant D PQ can be expressed as that of a product of twoCauchy-like matrices. One can then use the elementary exact formula for theCauchy determinant. One of course regains the known result, originallyconjectured in 1989.

Author: ** R.J. Baxter**

Source: https://arxiv.org/