Here is a paper I wrote about the Ising model. It contains some statements and some formalisations of results that are often referenced but rarely cited. It introduces MFT in a nice way and is fairly self-contained; I hope it can serve as a reference for those learning about the Ising model or mean field techniques.

This has now been published in SciPost Physics Lecture Notes, a diamond open access journal with counterparts in both physics and mathematics (publishing some very interesting mathematical physics lately). Magnetisation and Mean Field Theory in the Ising Model can be found at SciPost Physics Lecture Notes, 35, 2022.

See also the arXiv link, preprint arXiv:2102.00960.