Matter & Flow

The Magnet Machine

See how individual spins form domains—and how they add up to a magnet.

Presets set temperature and zero the field. Let the spins settle to compare.

Whole material

128 × 128 spins

Inside the selection

6 × 6 spins

Up spin Down spin

Tap or drag to inspect a patch. With the material focused, arrow keys move the selection. Pause before painting to keep your changes still.

How the spins add up

Net magnetization

Change the conditions

Set the magnetic conditions

Temperature T 2.27

Zero-field transition near T = 2.269. This finite material takes time to settle.

External field h 0.00

No preferred direction from an external field.

Sweeps per frame 8

Each sweep attempts one spin flip per site on average. These updates are not a physical clock.

Prepare the spins

Preparation changes the spins, not the temperature. Reset restores the same mixed starting pattern at your current settings.

TRY THIS

Choose Cool, then Align spins. Switch to Hot and watch the arrows lose their shared direction. Compare the balance below the material.

What you are seeing

Individual spins → domains → a magnet

Each site can point up or down. Nearby spins prefer to align, while thermal fluctuations can flip them. Patches with the same direction are magnetic domains.

The magnifier shows the exact 36 spins inside the outlined patch. The balance counts every spin in the material: equal numbers cancel, while a majority gives net magnetization. Large opposite domains can cancel even when each domain is ordered.

The lattice wraps at its edges. These are Monte Carlo samples of a two-dimensional Ising model, not literal pictures of atoms moving in time. A nonzero field favors one direction; the quoted transition temperature applies at zero field.