Spontaneous Magnetization of the Integrable Chiral Potts Model

Details Spontaneous Magnetization of the Integrable Chiral Potts Model Spontaneous Magnetization of the Integrable Chiral Potts Model

2010-03-25

arxiv.org/abs/1003.4805v2

Physics

Mathematical Physics

LaTeX 2E document, using iopart.cls with iopams packages, 22 pages, 1 eps figure. Presented at the Simons Center for Geometry

Scientific paper

We show how $Z$-invariance in the chiral Potts model provides a strategy to calculate the pair correlation in the general integrable chiral Potts model using only the superintegrable eigenvectors. When the distance between the two spins in the correlation function becomes infinite it becomes the square of the order parameter. In this way, we show that the spontaneous magnetization can be expressed in terms of the inner products of the eigenvectors of the $N$ asymptotically degenerate maximum eigenvalues. Using our previous results on these eigenvectors, we are able to obtain the order parameter as a sum almost identical to the one given by Baxter. This gives the known spontaneous magnetization of the chiral Potts model by an entirely different approach.

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