School Seminars and Colloquia

currently working with "Exactly Solved Models in Statistical Mechanics", by R.J. Baxter

Tuesday Seminar

by Nick Witte


Institution: Department of Mathematics and Statistics, The University of Melbourne
Date: Tue 12th October 2010
Time: 1:00 PM
Location: Room 213, Richard Berry Building, The University of Melbourne

Abstract: Many aspects of the the tradition derivations for the 6-vertex model and others from the time of Baxter's studies which go under the name of "ansatz" are mysterious and arbitrary. They often raise legitimate questions which are swept under the carpet, under the rationalisation that it works, it's correct and we are happy with the answer.

However there are very interesting implications of these questions and I will treat one example - the parameterisation of the 6-vertex model as a manifestation of a particular non-uniform discrete lattice, the q-quadratic lattice, which is the master case of a geometrical classification of non-uniform lattices. This then posits the TQ relation as a second-order divided difference equation on this lattice with a divided-difference operator, known as the Askey-Wilson operator.
This in turn opens up the vista of polynomial solutions to second-order divided-difference equations, with a history going back to Heine, Stieltjes and Hilbert.

Format:
Reading group. Interested participants each present a part of the literature.

For More Information: contact: Anita Ponsaing [a.ponsaing@ms.unimelb.edu.au]