A typical undergraduate course on statistical mechanics is arguably misleading because (unintentionally) it does not tell students several important things (related to one another).
Statistical mechanics is not just about how to calculate thermodynamic properties of a collection of non-interacting particles.
A hundred years ago, many physicists did not believe that statistical mechanics could describe phase transitions. Arguably, this lingering doubt only ended fifty years ago with Wilson's development of renormalisation group theory.
It is about emergence: how microscopic properties are related to macroscopic properties.
Leo Kadanoff commented, "Starting around 1925, a change occurred: With the work of Ising, statistical mechanics began to be used to describe the behaviour of many particles at once."
When I came to UQ 25 years ago, I taught PHYS3020 Statistical Mechanics a couple of times. To my shame, I never discussed the Ising model. There is a nice section on it in the course textbook, Thermal Physics: An Introduction, by Daniel Schroeder. I guess I did not think there was time to "fit it in" and back then, I did not appreciate how important the Ising model is. This was a mistake.
Things have changed for the better due to my colleagues Peter Jacobson and Karen Kheruntsyan. They now include one lecture on the model, and students complete a computational assignment in which they write a Monte Carlo code to simulate the model.
This year, I am giving the lecture on the model. Here are my slides (not including what I will write on the whiteboard or document viewer in the lecture).
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