The Ising model is a model of how magnets work at the atomic level, and is an interesting physical problem with a complicated solution. If you actually try to solve this problem analytically (i.e. with pen and paper), it would actually take longer than the age of the universe, but with Monte Carlo algorithms you can solve it in a reasonable time (you also end up with cool visualizations).

The plot below shows how the magnetization of the system evolves over time for two different systems. I let the simulations run for a period of time before plotting the results, so the magnetizations appear to fluctuate around a certain magnetization value: