Prof Jacques H.H. Perk, Oklahoma State University
The superintegrable chiral Potts chain is a parafermionic generalization of the spin-1/2 Ising chain in transverse field resulting from a search for solutions of the star-triangle (Yang--Baxter) equations for spin models. It has phase transitions from ordered and disordered states into an incommensurate state. Much progress has been made recently, explicitly constructing the eigenvectors in the commensurate ground state sector, using underlying quantum loop algebra structure. The two conjectures made in this construction have since been proved. This result has led to an explicit derivation of the spontaneous magnetization and some preliminary results for equal-time pair correlations. Very recently, we have done detailed analytic finite-size calculations to understand the full set of eigenvectors. Unlike the related XXZ model, the superintegrable chiral Potts chain has no Takahashi-like string states.
Based on work done with Helen Au-Yang.