Windowsill Lab · Field Explainer · M01

The temperature where
a magnet forgets itself

Heat a magnet and at some point it stops being a magnet — is that a gradual fade, or does it happen at one sharp temperature you can point to?

2.300measured
2.2692exact
40independent reruns
An oil-painted sheet of fine metallic scale-mail on a windowsill, one half settled into a uniform brass sheen, the other broken into scattered mismatched glints, with a turbulent band between them.
Illustration (AI-painted) — the temperature where agreement collapses

A magnet is a crowd of tiny compass needles, each one either pointing up or pointing down. Every needle would rather agree with the four neighbours touching it. Heat is the thing that makes them disagree — the hotter the sheet, the more often a needle flips against its neighbours just because it can.

Turn the heat down far enough and agreement wins: nearly the whole sheet points one way and the material is magnetic. Turn it up far enough and heat wins: the needles point every which way, the agreements cancel, and there is no magnetism left at all. The question is what happens in between. You might expect the magnetism to fade out smoothly over a wide band of temperatures. It doesn't. It collapses at one specific temperature, and above that temperature it is exactly zero.

That temperature is the thing this experiment measures. It has an exact known answer — Lars Onsager solved this model by hand in 1944 and found the tipping point sits at 2.2692 in the model's own units. Nothing in the run is told that number. The run heats the sheet through a range of temperatures, watches how wildly the magnetism swings at each one, and reports the temperature where the swinging is worst.

The panel below is that sheet, running live — the same checkerboard-Metropolis rule the graded run uses, seeded and stepping in your browser. Drag the temperature and watch it cross over. The interesting frame is not the cold one or the hot one — it's the middle one, where patches of agreement appear at many sizes at once and none of them last.

Live · square-lattice Ising · checkerboard Metropolis SMALL LATTICE — THE REAL RUN USED L=128
T = 1.600

left · the sheet (ember = up, bark = down) · right · |m| against temperature. Ember dots are measured here, in this tab: park the slider anywhere and the panel settles, then records a point. The slate curve is the exact answer (Yang 1952), the dashed vertical is Onsager's 2.2692, and the brass ring is where you are standing right now. Above T_c the measured dots sit a little above the exact zero: a finite sheet's |m| never quite reaches zero, and that floor shrinks as the lattice grows.

settling…

2.300measured T_c, χ peak MEASURED
±0.05quoted spread on the peak
32 swall time on GPU MEASURED
25nightly reruns captured
40receipts on file

The graded run reports the tipping point at 2.300, within its own quoted spread of ±0.05 of Onsager's exact 2.2692 — and it gets there without ever being told the answer, by sweeping temperature and asking only where the magnetism swings hardest. It is the most-repeated experiment on this instrument: 25 nightly reruns, 40 receipts on file.

Temperature here is in the model's own units, not degrees — this is a lattice of abstract spins, not a lump of iron, and 2.2692 is a pure number. The measured peak sits just above the exact value because the lattice is finite; that shift is expected physics, not error, and it shrinks as the lattice grows. The exact magnetization curve drawn alongside the measured points is C. N. Yang's 1952 result — Onsager's 1944 paper gives the free energy and the critical temperature, not the curve. One 2026-07-23 pass produced a spuriously low answer from a single lattice frozen in a system-spanning stripe; the checker has carried a non-equilibration guard ever since.
Next on the ladder: M02 — the peak grows on schedule M04 — a second, independent needle M10 — the same tipping point, invisible