Kramers-Wannier Duality and Factor Graphs.

We consider the classical duality result of Kramers and Wannier, which expresses the partition function of the two-dimensional Ising model at low temperature in terms of the partition function of the two-dimensional Ising model at high temperature. Our main contribution is to gain new insights into this result by reproving it with the help of a simple normal-factor-graph duality theorem (with origins in coding theory), together with some elementary notions from algebraic topology. An important ingredient of our proof approach are normal-factor-graph representations of some notions from algebraic topology; a side contribution of this paper is to elaborate on such representations. In addition to the two-dimensional Ising model, we also discuss the three-dimensional Ising model and the Potts model.