A Pedagogical Discussion of Magnetisation in the Mean Field Ising Model

Dalton A R Sakthivadivel

Published 2021-01-29Version 1

Here, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with the motivation and basis for mean field theory, we formally derive the Bogoliubov inequality and discuss mean field theory itself. We proceed with the use of mean field theory to determine Ising magnetisation, and the results of the derivation are interpreted graphically and physically. We include some more general comments on the thermodynamics of the phase transition. We end by evaluating symmetry considerations in magnetisation, and some more subtle features of the Ising model. Together, a self-contained overview of the magnetised Ising model is presented, with some novel presentation of important results.