A conjecture for the superintegrable chiral Potts model
arXiv:0803.4037 · doi:10.1007/s10955-008-9588-x
Abstract
We adapt our previous results for the ``partition function'' of the superintegrable chiral Potts model with open boundaries to obtain the corresponding matrix elements of e^{-αH}, where H is the associated hamiltonian. The spontaneous magnetization M_r can be expressed in terms of particular matrix elements of e^{-αH} S^r_1 \e^{-βH}, where S_1 is a diagonal matrix.We present a conjecture for these matrix elements as an m by m determinant, where m is proportional to the width of the lattice. The author has previously derived the spontaneous magnetization of the chiral Potts model by analytic means, but hopes that this work will facilitate a more algebraic derivation, similar to that of Yang for the Ising model.
19 pages, one figure; Corrections made between 28 March 2008 and 28 April 2008: (1) 2.10: q to p; (2) 3.1: epsilon to 0 (not infinity); (3) 5.29: p to q; (4) p14: sub-head: p, q to q,p; (5) p15: sub-head: p, q to q,p; (6) 7.5 second theta to -theta ; (7) before 7.6: make more explicit definition of lambda_j. Several other typos fixed later
References in corpus (4)
Cited by in corpus (9)
- 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
- 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
- Spin operator matrix elements in the superintegrable chiral Potts quantum chain
- Algebraic reduction of the Ising model
- Spontaneous Magnetization of the Integrable Chiral Potts Model
- Some comments on developments in exact solutions in statistical mechanics since 1944