String melting of the floating phase in antiferromagnetic clock models

In two-dimensional antiferromagnetic q-state clock models with odd values of q=5,7,9,. . . on a square lattice, the low-temperature phase is a floating solid, with impurities and logarithmically bound vortices. Both are composite objects. Inside their cores they contain vertices of vorticity 0 and ±{}q bound together by linear interactions induced by strings. The meander entropy of these strings competes with the positional entropy of the composite vortices. Kosterlitz-Thouless melting is preempted by a string-melting transition, where the cores of the vortices and impurities diverge.