The order parameter of the chiral Potts model

Abstract

An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but as far as the author is aware there is as yet no proof of the conjecture. Here we show that if one makes a certain analyticity assumption similar to that used to derive the free energy, then one can indeed verify the conjecture. The method is based on the ``broken rapidity line'' approach pioneered by Jimbo, Miwa and Nakayashiki.

29 pages, 7 figures. Citations made more explicit and some typos corrected

References in corpus (1)

• Transfer matrix functional relations for the generalized tau_2(t_q) model

Cited by in corpus (22)

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• Eigenvectors in the Superintegrable Model I: sl_2 Generators
• Some remarks on a generalization of the superintegrable chiral Potts model
• The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
• Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D_PQ
• The Ferromagnetic Potts model under an external magnetic field: an exact renormalization group approach
• Spin operator matrix elements in the superintegrable chiral Potts quantum chain
• Identities in the Superintegrable Chiral Potts Model
• Transfer matrix eigenvectors of the Baxter-Bazhanov-Stroganov ${\tau }_2$-model for N=2
• A conjecture for the superintegrable chiral Potts model
• The Transfer Matrix of Superintegrable Chiral Potts Model as the Q-operator of Root-of-unity XXZ Chain with Cyclic Representation of $U_q(s{l}_2)$
• Algebraic reduction of the Ising model
• Some ground-state expectation values for the free parafermion Z(N) spin chain
• The challenge of the chiral Potts model
• Pivoting through the chiral-clock family
• Spontaneous Magnetization of the Integrable Chiral Potts Model
• Some comments on developments in exact solutions in statistical mechanics since 1944
• Bethe ansatz solution of the ${\tau }_2$-model with arbitrary boundary fields
• Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models
• Correlation functions for the three state superintegrable chiral Potts spin chain of finite lengths
• Duality and Symmetry in Chiral Potts Model
• Free energy of the three-state ${\tau }_2(t_q)$ model as a product of elliptic functions