The glass transition
that has not shown up yet

M11 showed a frustrated magnet in two dimensions, where theory says no glass phase can survive above absolute zero. Add a third dimension and the physics changes: the glass transition becomes real, at a finite temperature, and the literature has pinned it. For the bimodal ±J couplings this engine simulates, the benchmark is T_SG ≈ 1.102. That number is the target, and this milestone has not hit it.

The signature everyone uses is a Binder cumulant crossing. Run the same system at several lattice sizes, plot a particular ratio of overlap moments against temperature, and watch the curves. Away from a transition, bigger lattices sit systematically above or below smaller ones. At a transition they all pass through one point. So the crossing is the transition, and finding it means finding one place where four curves agree. In four runs, this instrument's curves have crossed at 0.56 (twice — the two quick CPU passes share that crossing), at 1.244, and most recently at 1.221 — never cleanly at 1.10.

The reason the cold end is hard is that a frustrated magnet gets stuck. Single-spin updates at low temperature can spend the entire run trapped in one valley of an enormously rugged landscape. The standard cure is parallel tempering: run a whole ladder of temperature copies at once and let neighbouring rungs periodically swap configurations, so a frozen cold copy gets carried up to where it can move, shuffled, and brought back down. It is a beautiful idea and it is exactly where this milestone's most instructive failure lived.

A 2026-08-01 audit found two defects that invalidated the 2026-07-22 run as a promotion gate. The first is the one worth putting on a web page: the swap scheduler derived its parity from the sweep index, so the production default of swapping every 10 sweeps pinned that parity to zero forever, and every odd-gap pair of rungs was never attempted. The ladder silently decomposed into isolated two-rung pairs that could never mix along its length — visible in the receipt as exactly 0.0 at every odd gap of the swap-rate table. The second defect is quieter and just as fatal: the run was graded against 0.95, the Gaussian-disorder value, while simulating bimodal ±J couplings. Even a perfectly converged run landing on the correct ≈1.102 could not have passed.

The panel below lets you switch that first bug on and watch a working ladder fall apart.

Turn the bug on and the ladder stratifies within seconds: rungs 0↔1 keep swapping, 2↔3 keep swapping, and nothing ever crosses between those cells. The odd-gap swap rate goes to exactly 0.000 — not "small", not "rare", but the hard zero the 2026-07-22 receipt recorded, because those pairs were never attempted. Turn the swap interval to an odd number and the bug stops biting, which is why the earlier CPU runs at swap_every=5 were unaffected by it.

The latest attempt — 2026-08-15, L = 6, 8, 10, 12 across 500 disorder realizations with parallel tempering, 2140 seconds of wall time — put the crossing at 1.221 against a configured band of 1.10 ± 0.10. That is still a null. The literature values it is being measured against are 1.1019(29) from Hasenbusch–Pelissetto–Vicari and 1.120(4) from Katzgraber–Körner–Young; the 0.951(9) the 2026-07-22 run was graded against is Katzgraber–Körner–Young's Gaussian-disorder value, and using it on a bimodal run meant even a perfectly converged result could not have passed.

Promotion needs all three of: the parity fix and corrected benchmark merged, a fresh multi-size run landing inside the corrected tolerance, and human review of that run. The 2026-08-15 run does not clear it. Nothing on this page is a measurement of T_SG; it is an open measurement and the audit that reopened it. The two-dimensional case, where theory says there is nothing to find above absolute zero, is M11 — and that one is green.