Some remarks on a generalization of the superintegrable chiral Potts model
نویسنده
چکیده
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.
منابع مشابه
The Transfer Matrix of Superintegrable Chiral Potts Model as the Q-operator of Root-of-unity XXZ Chain with Cyclic Representation of Uq(sl2)
We demonstrate that the transfer matrix of the inhomogeneous N -state chiral Potts model with two vertical superintegrable rapidities serves as the Q-operator of XXZ chain model for a cyclic representation of Uq(sl2) with Nth root-of-unity q and representation-parameter. The symmetry problem of XXZ chain with a general cyclic Uq(sl2)-representation is mapped onto the problem of studying Q-opera...
متن کاملThe Onsager Algebra Symmetry of Τ -matrices in the Superintegrable Chiral Potts Model
We demonstrate that the τ (j)-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of the eight-vertex model for roots of unity and the superintegrable chiral Potts model has been carefully analyzed by identifying equivalent terms in the corresponding equations, by which w...
متن کامل2 9 M ay 2 00 5 The Onsager Algebra Symmetry of τ ( j ) - matrices in the Superintegrable Chiral Potts Model
We demonstrate that the τ (j)-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of eight-vertex model for roots of unity and superintegrable chiral Potts model has been carefully analyzed by identifying equivalent terms in the corresponding equations , by which we extra...
متن کاملThe L(sl2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model
The loop algebra L(sl2) symmetry is found in a sector of the nilpotent BazhanovStroganov model. The Drinfeld polynomial of a L(sl2)-degenerate eigenspace of the model is equivalent to the polynomial [4, 5, 10–14] which characterizes a subspace with the Isinglike spectrum of the superintegrable chiral Potts model.
متن کاملFinite-size energy levels of the superintegrable chiral Potts model
In the solution of the superintegrable chiral Potts model special polynomials related to the representation theory of the Onsager algebra play a central role. We derive approximate analytic formulae for the zeros of particular polynomials which determine sets of low-lying energy eigenvalues of the chiral Potts quantum chain. These formulae allow the analytic calculation of the leading finite-si...
متن کامل