Chiron / The Ising Model

2D Ising Model

A lattice of magnetic spins flipping by the Metropolis rule. Cool it and domains align into a magnet; heat past the critical temperature (Tc ≈ 2.269) and order dissolves into noise. Ported from my undergrad computational-physics C/OpenGL coursework.

Temperature
2.27
Magnetisation
…
Energy / spin
…
Lattice
…

Magnetisation curve  |M| vs temperature

Space play/pause · R reset. Auto-sweep ramps T from cold to hot, plotting the average |M| at each step. The sharp drop near Tc is the phase transition.

Things to notice

Frozen stripes

Quench it from hot straight down to near-zero and the lattice can jam into stripes: domain walls it's gone too cold to remove.

Why this happens

Critical slowing down

Right at Tc the lattice never settles: domains of every size churn endlessly and the |M| dot jitters instead of holding still.

What you're seeing

It picks a side

With no field, cooling from random freezes the lattice mostly-gold or mostly-dark, at random. Reset a few times and watch it choose.

The deeper idea