Feynman's Formula for the Ising Model on Surfaces

This is my final submission for the mini-thesis that formed part of my BScHons (Mathematics) degree.

The essay is a pedagogical expository account of the results of a paper by Chelkak, Cimasoni, & Kassel (2017) which develops a combinatorial proof of the generalized Kac-Ward formula for the high-temperature polynomial of an Ising model embedded on an arbitrary surface.

Aside from giving a more thorough introduction, my mini-thesis expands on the results of the paper by filling in a few of the omitted proofs. Still, the mini-thesis should generally not be considered original work, since none of the ideas are my own.