A Factor-Graph Approach to Algebraic Topology, With Applications to Kramers–Wannier Duality
2018
Algebraic topology studies topological spaces with the help of tools from abstract algebra. The main focus of this paper is to show that many concepts from algebraic topology can be conveniently expressed in terms of (normal) factor graphs. As an application, we give an alternative proof of a classical duality result of Kramers and Wannier, which expresses the partition function of the 2-D Ising model at a low temperature in terms of the partition function of the 2-D Ising model at a high temperature. Moreover, we discuss analogous results for the 3-D Ising model and the Potts model.
Keywords:
- Potts model
- Kramers–Wannier duality
- Discrete mathematics
- Combinatorics
- Dimension of an algebraic variety
- Computer science
- Function field of an algebraic variety
- Extension topology
- Nisnevich topology
- A¹ homotopy theory
- General topology
- Combinatorial topology
- Product topology
- Topological combinatorics
- Topological space
- Algebraic topology
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