Chiral Potts model information

The chiral Potts model is a spin model on a planar lattice in statistical mechanics studied by Helen Au-Yang Perk and Jacques Perk, among others. It may be viewed as a generalization of the Potts model, and as with the Potts model, the model is defined by configurations which are assignments of spins to each vertex of a graph, where each spin can take one of $N$ values. To each edge joining vertices with assigned spins $n$ and $n'$ , a Boltzmann weight $W(n,n')$ is assigned. For this model, chiral means that $W(n,n')\neq W(n',n)$ . When the weights satisfy the Yang–Baxter equation, it is integrable, in the sense that certain quantities can be exactly evaluated.

For the integrable chiral Potts model, the weights are defined by a high genus curve, the chiral Potts curve.^[1]^[2] Unlike the other solvable models,^[3]^[4] whose weights are parametrized by curves of genus less or equal to one, so that they can be expressed in terms of trigonometric functions, rational functions for the genus zero case, or by theta functions for the genus 1 case, this model involves high genus theta functions, for which the theory is less well-developed.

The related chiral clock model, which was introduced in the 1980s by David Huse and Stellan Ostlund independently, is not exactly solvable, in contrast to the chiral Potts model.

^ Au-Yang, Helen; McCoy, Barry M.; Perk, Jacques H. H.; Tang, Shuang; Yan, Mu-Lin (10 August 1987). "Commuting transfer matrices in the chiral Potts models: Solutions of star-triangle equations with genus>1". Physics Letters A. 123 (5): 219–223. doi:10.1016/0375-9601(87)90065-X. ISSN 0375-9601.
^ Baxter, R. J.; Perk, J. H. H.; Au-Yang, H. (28 March 1988). "New solutions of the star-triangle relations for the chiral potts model". Physics Letters A. 128 (3): 138–142. doi:10.1016/0375-9601(88)90896-1. ISSN 0375-9601. Retrieved 10 July 2023.
^ Baxter, Rodney J. (2007). Exactly solved models in statistical mechanics. Mineola, N.Y: Dover Publications, Inc. ISBN 978-0486462714.
^ McCoy, Barry M. (2010). Advanced statistical mechanics. Oxford: Oxford university press. ISBN 978-0199556632.

[AMPTY-1] Au-Yang, Helen; McCoy, Barry M.; Perk, Jacques H. H.; Tang, Shuang; Yan, Mu-Lin (10 August 1987). "Commuting transfer matrices in the chiral Potts models: Solutions of star-triangle equations with genus>1". Physics Letters A. 123 (5): 219–223. doi:10.1016/0375-9601(87)90065-X. ISSN 0375-9601.

[BPA-2] Baxter, R. J.; Perk, J. H. H.; Au-Yang, H. (28 March 1988). "New solutions of the star-triangle relations for the chiral potts model". Physics Letters A. 128 (3): 138–142. doi:10.1016/0375-9601(88)90896-1. ISSN 0375-9601. Retrieved 10 July 2023.

[Baxterbk-3] Baxter, Rodney J. (2007). Exactly solved models in statistical mechanics. Mineola, N.Y: Dover Publications, Inc. ISBN 978-0486462714.

[McCoybk-4] McCoy, Barry M. (2010). Advanced statistical mechanics. Oxford: Oxford university press. ISBN 978-0199556632.

Chiral Potts model information

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