PROOF OF THE DETERMINANTAL FORM OF THE SPONTANEOUS MAGNETIZATION OF THE SUPERINTEGRABLE CHIRAL POTTS MODEL

Author:

BAXTER R. J.

Abstract

AbstractThe superintegrable chiral Potts model has many resemblances to the Ising model, so it is natural to look for algebraic properties similar to those found for the Ising model by Onsager, Kaufman and Yang. The spontaneous magnetization ℳr can be written in terms of a sum over the elements of a matrix Sr. The author conjectured the form of the elements, and this conjecture has been verified by Iorgov et al. The author also conjectured in 2008 that this sum could be expressed as a determinant, and has recently evaluated the determinant to obtain the known result for ℳr. Here we prove that the sum and the determinant are indeed identical expressions. Since the order parameters of the superintegrable chiral Potts model are also those of the more general solvable chiral Potts model, this completes the algebraic calculation of ℳr for the general model.

Publisher

Cambridge University Press (CUP)

Subject

Mathematics (miscellaneous)

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Some academic and personal reminiscences of Rodney James Baxter;Journal of Physics A: Mathematical and Theoretical;2015-06-04

2. On the Form Factors of Local Operators in the Bazhanov–Stroganov and Chiral Potts Models;Annales Henri Poincaré;2014-10-22

3. The τ2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin’s SOV method;Journal of Statistical Mechanics: Theory and Experiment;2012-11-09

4. Spontaneous magnetization of the integrable chiral Potts model;Journal of Physics A: Mathematical and Theoretical;2011-10-14

5. Onsager and Kaufman’s Calculation of the Spontaneous Magnetization of the Ising Model;Journal of Statistical Physics;2011-05-13

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