We go back to physics and make a first encounter with a field theory defined as a lattice model, the Ising model. We introduce it and define it in the context of statistical mechanics. Students interested in the physics of the Ising model can find some further readings in the references.

Ising( $LaTeX: \beta$ ) Definition of statistical Ising model on a square lattice
The $LaTeX: \mathbb{Z}_2$ topological defect lines and their action on correlators and partition functions -- dependence on boundary conditions
Gauging the $LaTeX: \mathbb{Z}_2$ symmetry: the model Ising/ $LaTeX: \mathbb{Z}_2$ ( $LaTeX: \beta$ )
Kramers-Wannier Duality
Ising Category symmetry at the critical temperature and its action on correlators and partition functions

Lecture Notes: van Emmerik notes

References:

David Aasen, Roger S.K. Mong, Paul Fendley, Topological Defects on the Lattice I: The Ising Model, https://arxiv.org/abs/1601.07185.

Nils Carqueville, Michele Del Zotto, Ingo Runkel, Topological Defects, https://arxiv.org/abs/2311.02449

Subir Sachdev, Quantum Phase Transitions, Freely available with our library