The Ising model

A real-time visualization of the Ising model for a two-dimensional grid of half-integer spin particles. You can control inverse temperature to discover the ferromagnetic phase transition. The model for the hamiltonian $H$ corresponding to the spins $\sigma_i$ is \[ H = \sum_{\langle i j \rangle}J_{ij} \sigma_i \sigma_j \] where $\langle i j \rangle$ refers to neighbouring lattice sites, and $J_{ij}=1$ for all $i,j$. I don't feel like writing more about this now, but you are invited to explore the implications of the model at e.g. wikipedia.