Funny behavior in the Ising model

[Despite first appearances, I promise that the humor here is reasonably accessible to non-physicists.]

The last homework assignment in my statistical mechanics class asked the students to write a computer program to simulate the simple Ising model of a ferromagnet. You model the magnetic material as an array of sites that are "spin up" and "spin down", and the simulation produces images showing how the up (black) and down (white) sites are distributed for various temperatures. Below a certain "critical temperature" the system is mostly magnetized; above that temperature, it becomes increasingly random. Especially interesting things happen right at (or very near) the critical temperature.

A couple of my students found some particularly unexpected results as the temperature approached this special value. Things went pretty much as expected as T decreased closer and closer to the critical temperature (the cluster size gets larger and larger, for example):



But when they made that last temperature change as described at the end of the page scanned above, it led to a result that I didn't expect at all:
( At the 'critical temperature' T=Mr )

I've gotta say, my students can be pretty cool.