Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy they show analytically the critical singularity near the phase transition in the anti-ferroelectric regime, where the essential singularity similar to the Kosterlitz-Thouless transition appears. They discuss the connection of the six-vertex model to the conformal field theory with c=1. They also introduce various exactly solvable models defined on two-dimensional lattices such as the chiral Potts model and the IRF models. We show that the six-vertex model has rich mathematical structures such as the
quantum groups and the braid group.
The graphical approach is emphasized in this review. |