At zero temperature, or the β β → → ∞ ∞ limit, all the plaquettes will contain exactly one negative edge. In this case, on each checkered plaquette, the KBD algorithm will always open two parallel bonds perpendicular to the negative edge, meaning that the bond will be closed on the negative edge along with the edge opposite to it. If we were to track the closed bonds in the dual lattice, by drawing a straight/bent line inside each plaquette such that it intersects with the closed bonds, then it can be shown that a path following the lines must form a cycle.