# The Tutte polynomial and the Potts model in square lattices

*by Arun Mani*

*Institution:*Clayton School of IT, Monash University

*Date: Tue 15th June 2010*

*Time: 1:00 PM*

*Location: Room 213, Richard Berry Building, The University of Melbourne*

*Abstract*: The Tutte polynomial of a graph is a polynomial in two

variables, $x,y$, that is of central importance in many counting problems. The Potts model partition function is known to be computationally equivalent to an evaluation of the Tutte polynomial

along the curve $(x-1)(y-1) = q$ for integer values of $q$. The asymptotic growth of the Tutte polynomial (and the Potts model) of a square lattice as its dimensions tend to infinity are often of special interest in combinatorics and statistical physics. In this talk we

introduce a family of inequalities for the Tutte polynomial of square lattices, and apply them to obtain non-trivial one-sided bounds for a limit describing this growth when $x, y \geq 1$.

*For More Information:* contact Iwan Jensen. email: i.jensen@ms.unimelb.edu.au