Furthermore, it can be shown that there must be at least two such cycles, and that the cycles cannot intersect. Most importantly, each cycle cannot be contracted to a point in the underlying surface that the lattice is embedded in. On a periodic lattice (or a torus), this means that the cycles of closed bonds must wind around the torus in the same direction, from which one can show that the largest cluster (which must be "squeezed" between these cycles) at zero temperature cannot span a finite fraction of the lattice size in the thermodynamic limit.