A Factor-Graph Approach to Algebraic Topology, With Applications to Kramers--Wannier Duality
نویسندگان
چکیده
We consider the classical duality result of Kramers and Wannier, which expresses the partition function of the twodimensional 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 normalfactor-graph duality theorem (with origins in coding theory), together with some elementary notions from algebraic topology. An important ingredient of our proof approach are normalfactor-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.
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