Magnetisation and Mean Field Theory in the Ising Model
Abstract
In this set of notes, a complete, pedagogical tutorial for applying mean field theory to the twodimensional 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 a magnetisation function, and the results of the derivation are interpreted graphically, physically, and mathematically. We give a new interpretation of the selfconsistency condition in terms of intersecting surfaces and constrained solution sets. We also 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 selfcontained overview of the mean field Ising model is given, with some novel presentation of important results.
 Publication:

arXiv eprints
 Pub Date:
 January 2021
 arXiv:
 arXiv:2102.00960
 Bibcode:
 2021arXiv210200960S
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 20 pages, two figures. Revisions to presentation