Hysterainy

I've been enduring a lot of rain lately, both in Italy, and now back in Annecy. I'm always frustrated by intermittent rain, since I have to wonder whether it's worthwhile to open/close my umbrella when the rain starts/stops. Whenever I start thinking about it, I'm reminded of the idea of magnetic hysteresis. This is the tendency of magnetic systems to "remember" the state they were in earlier, even when outside conditions change.

The classic model system for this is the Ising model, which I discussed in an earlier post. The difference here is that we vary the external field and see how the system's internal field reacts. The typical plot looks like this:

Based on Wikipedia

On the x-axis is the applied external field (how much it's raining), and on the y-axis is the field within the system (how likely I am to have my umbrella open). Starting in the center, with both fields zero, we slowly increase the external field, which brings the system along with it. When we decrease the field though, the system lags behind, still giving a positive field when the external one is negative, just like keeping my umbrella up while it's not raining.

I decided to adapt my previous Ising script to try to demonstrate this effect, and I was surprised by my success: Hysteresis.py

On the left is the grid of magnetic spins, which interact with their neighbors and the external field. On the right is a plot of the external field vs the average field of the spins. Aside from the weird jiggling frame I couldn't get rid of, it matches the model above pretty well!

Marika and I are packing things up to return to the States in a couple weeks, so I may miss posting.