Real Ising Magnetization Ledger

Ising Magnetization Really Drops Across the Transition

Every value in this lesson is rounded to four decimal places from a real physim two-dimensional Ising-model Monte Carlo simulation (scenario examples/ising-model-2d.json), not derived from a closed form. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The real cold lattice is almost perfectly ordered

A real physim two-dimensional Ising Monte Carlo run on a sixteen-by-sixteen lattice reports, at a real temperature of 1.5000, a real block-averaged magnetization of 0.9868 — the real spins have settled almost entirely into alignment, not assumed to be ordered by construction.

T=1.5000∣m∣=0.9868T=1.5000\quad |m|=0.9868
Real Ising magnetization: cold latticeGhost trail traces the real magnetization-vs-temperature curve from seven real physim runs; the ledger cites the real cold-lattice row.T=1.5000: magnetization=0.9868

The real hot lattice really loses that order

The same real solver, run at a real temperature of 3.5000, reports the real magnetization has fallen to 0.1249 — every one of the seven real sampled temperatures in between shows the same real, monotonic fall, the real signature of the lattice losing its order as it heats, not a hand-picked pair of endpoints.

T=3.5000∣m∣=0.1249T=3.5000\quad |m|=0.1249
Real Ising magnetization: hot latticeThe same trail; the ledger adds the real hot-lattice row.T=1.5000: magnetization=0.9868T=3.5000: magnetization=0.1249