A strange mathematical model proves that heat can actually create perfect order instead of destroying it.
Standard thermodynamics says that as you heat something up, it becomes more chaotic and disordered. This research shows that in certain lattice models, high temperatures actually force the system into a perfect checkerboard pattern. This order by disorder happens because the system finds more ways to be ordered than it does to be messy. This effect persists even at temperatures that would normally melt or vaporize any known substance. It challenges our basic intuition about how entropy works in the universe.
Order by disorder up to arbitrarily high temperature
arXiv · 2604.28026
We prove that a class of classical lattice models on $\mathbb{Z}^d$ ($d \geq 2$) with on-site space $\mathbb{N}_0$ exhibits long-range checkerboard order at sufficiently high temperature. The model has a nearest-neighbour interaction $f : \mathbb{N}_0 \times \mathbb{N}_0 \to [0,\infty)$ satisfying four structural conditions, subsuming the recently introduced power-law model of Han--Huang--Komargodski--Lucas--Popov (arXiv:2503.22789) as a special case. The ordering mechanism is purely entropic: t