Entropic order

Ordered phases of matter, such as solids, ferromagnets, superfluids, or quantum topological order, typically only exist at low temperatures. Despite this conventional wisdom, we present explicit local models in which all such phases persist to arbitrarily high temperature. This is possible since order in one degree of freedom can enable other degrees of freedom to strongly fluctuate, leading to entropic order. Using interacting bosons, we construct local lattice models to display this entropic order that is provably stable against classical/quantum perturbations. Finally, we discuss how such models could be realized and probed in cold-atom experiments.