The 2D XY model has no conventional order but a topological phase transition (Berezinskii-Kosterlitz-Thouless). Below T_BKT, vortex-antivortex pairs bind; above, they unbind and proliferate, destroying quasi-long-range order.
Arrows: spin directions. Red dot=vortex (+1), Blue dot=antivortex (-1). T_BKT ≈ 0.89 for XY model.