Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D_PQ

Abstract

For the Ising model, the calculation of the spontaneous magnetization leads to the problem of evaluating a determinant. Yang did this by calculating the eigenvalues in the large-lattice limit. Montroll, Potts and Ward expressed it as a Toeplitz determinant and used Szego's theorem: this is almost certainly the route originally travelled by Onsager. For the corresponding problem in the superintegrable chiral Potts model, neither approach appears to work: here we show that the determinant D_PQ can be expressed as that of a product of two Cauchy-like matrices. One can then use the elementary exact formula for the Cauchy determinant. One of course regains the known result, originally conjectured in 1989.

16 pages, no figures; revised 11 Jan 2010 to correct citations and to include reference to subsequent work

References in corpus (1)

• An algebraic derivation of the eigenspaces associated with an Ising-like spectrum of the superintegrable chiral Potts model

Cited by in corpus (10)

• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Onsager and Kaufman's calculation of the spontaneous magnetization of the Ising model
• Exact and simple results for the XYZ and strongly interacting fermion chains
• The square lattice Ising model on the rectangle I: Finite systems
• Spin operator matrix elements in the quantum Ising chain: fermion approach
• Form-factors of the finite quantum XY-chain
• The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
• Spin operator matrix elements in the superintegrable chiral Potts quantum chain
• Spontaneous Magnetization of the Integrable Chiral Potts Model
• Some comments on developments in exact solutions in statistical mechanics since 1944