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So, today’s BMC post will touch on a topic near and dear to all my readers hearts: magnets, how do they work? Well, dear reader, they are not in fact miracles, but the result of the interactions of spin lattices that can be described using the Ising model of magnetism. I shall endeavor to explain a few key features of this model to you, and let you know about a few cool things we can do with it.

### Spin and Magnetism

So, we are all good atomists by now, and we know that the aggregate behavior of a an object is often the effect of changes in the particles making up that object. Whether that change is something strange like Bose-Einstein Condensation or something more mundane, like phase change, the whole of statistical physics relies on the idea that we can get macroscopic observables out of microscopic properties. One of the microscopic properties that particles can possess is spin. This is a quantum number often compared to angular momentum, but it isn’t really analogous to classical angular momentum, just like quantum chromodynamics isn’t really about color. This spin, however, does give the particle a magnetic dipole moment, making it act like a tiny bar magnet. By looking at the statistical properties of individual particles and their spin, you can describe the macroscopic magnetic behavior of an object.

### Ernst Ising and His Fantastic Model

In order to use the microscopic spin properties to explain macroscopic magnetism, Ernst Ising and his doctoral adviser, Wilhelm Lenz developed the Ising model in the mid 1920s. The model worked by considering each pair of particles, and whether they liked sharing a common spin (ferromagnets), liked having opposite spins (antiferromagnets), or if they are non-interacting. This allowed the calculation of energy as a function of the spin alignments, and with that the whole arsenal of statistical mechanics tools could be used to examine magnetism.

### What it Tells Us

Using the Ising model, a number of experimentally observed properties were easily predicted. First, it allowed a way of describing why some materials are easily magnetized (ferromagnets like iron and nickel), while others seemed to shrug off magnetic fields (like chromium). The ferromagnets are in a lower energy state when their spins are aligned, and thus like to become magnetized, while antiferromagnets do not. More interesting was the ability for it to predict a phase transition from magnetic to non-magnetic at a certain temperature (the Curie point). This was the first time a phase transition was described using the Canonical Partition Function. Most interesting (to me) is the ability to use this model to describe neural networks in AI and brain research. I bet Ising never expected *that *application!