Solvable Models on Regular and Random Lattices in Statistical Mechanics and Field Theory

There are only a few solvable models in statistical mechanics and field theory, but those that are known give deep insights into the cooperative behaviour that characterizes a critical point, as well as leading to fascinating mathematics. The two chief investigators have been at the forefront of this field for many years. Currently there are many notable exciting challenges they wish to address: the relationship between Tutte's work on dichromatic polynomials and matrix models, the outstanding problem of calculating the order parameters of the chiral Potts model, and the eigenvalue spectra of the transfer matrices that occur in integrable models.