Ising ModelA toy magnet: a grid of tiny compass needles, each wanting to point the same way as its neighbours while heat jostles them at random. Cold, they all line up into big blocks. Hot, it’s pure static. At one exact temperature in between, blocks of every size coexist — the material is on a knife-edge.Ernst Ising solved the 1D chain in 1925 and wrongly concluded magnets never work. Rudolf Peierls (1936) showed 2D is different, and in 1944 Lars Onsager pulled off one of physics’ hardest exact solutions, pinning the tipping point at 2 ÷ ln(1+√2). The same maths now describes alloys, neurons, and flocking birds.