The Two-Valued Spin and Its One Neighbour: Lenz and Ising's Postulated Magnet, Priced

In 1920 Wilhelm Lenz simplified the magnet to two-valued variables on a lattice, and in 1925 Ernst Ising solved the one-dimensional case of that simplification in his doctoral thesis, a problem suggested to him by Lenz. I credit those papers at full strength: they produced the first exactly soluble model of a magnet, an exact negative result in one dimension, and, through the later exact two-dimensional solution at this same address, the founding landmark of the modern theory of critical phenomena and universality. Nothing in this paper falsifies a result derived inside the model, and nothing in it disputes the model's organising power. What I price is the standing of the model itself in 1920 and 1925. A magnet is replaced, by postulation, with variables sigma_i = ±1 on a lattice, interacting only as nearest neighbours through a single coupling J in H = -J sum over nearest-neighbour pairs of sigma_i sigma_j. The continuous moment, its transverse components, every longer-range interaction and every multi-spin interaction are deleted, and J is a free parameter that no step in 1920 or 1925 sets from the material. My bench prices what that postulation carries, on declared inputs only. In two dimensions, on a square lattice, the exact condition sinh(2/t_c) = 1 returns t_c = 2.269185, where t = k_B T / J, with sinh(2/t_c) = 1.000000 at that point; mean field, with coordination number z = 4, returns 4.000000, an overstatement of 76.274717 per cent. The spontaneous magnetisation in Yang's form is M = 0.999276 at t = 1, M = 0.911319 at t = 2 and M = 0.671854 at t = 2.25, and it is zero at and above t_c. In one dimension, Ising's own case, the exact critical temperature is 0.000000, while mean field, with z = 2, invents a transition at 2.000000; the correlation length xi/a = 27.296022 at t = 0.5, 3.671861 at t = 1, 1.295443 at t = 2 and 0.710818 at t = 4, finite at every temperature above zero. Counted plainly: 1 postulated Hamiltonian, carrying 1 fitted coupling and 2 deletion classes, against 0 derivations in 1920 and 1925. Grade for this census entry, printed at full size: **REASON FOUND / STILL TURNING** — PREMISE-ONLY, explicitly not a kill and not a falsification. The program headline stands unmoved: **vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.**