Swiss Knots 2011

Knot Theory and Algebra

Lake Thun, May 23-27

The generalized Kac-Ward formula

Dr. David Cimasoni's talk
Date: 26.05.11   Time: 11.20 - 12.10   Room: Gwatt Zentrum

Abstract: The Kac-Ward formula allows to compute the Ising partition function on a planar graph G with N straight edges from the determinant of a matrix of size 2N. In this talk, I will show how this formula can be extended to any finite graph: the partition function can then be written as an alternating sum of 4^g determinants, where g is the genus of a surface in which G embeds. I will also explain a natural link between this method of computation and the "Pfaffian method" of Fisher and Kasteleyn.