Some remarks on a generalization of the superintegrable chiral Potts model

Abstract

The spontaneous magnetization of a two-dimensional lattice model can be expressed in terms of the partition function $W$ of a system with fixed boundary spins and an extra weight dependent on the value of a particular central spin. For the superintegrable case of the chiral Potts model with cylindrical boundary conditions, W can be expressed in terms of reduced hamiltonians H and a central spin operator S. We conjectured in a previous paper that W can be written as a determinant, similar to that of the Ising model. Here we generalize this conjecture to any Hamiltonians that satisfy a more general Onsager algebra, and give a conjecture for the elements of S.

18 pages, one figure

References in corpus (1)

• The L(sl_2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model

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• Some comments on developments in exact solutions in statistical mechanics since 1944
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• A coupled Temperley-Lieb algebra for the superintegrable chiral Potts chain
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