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It is known that there is no phase transition down to zero temperature in theantiferromagnetic Ising model on spatially anisotropic triangular lattices, inwhich the exchange coupling of one direction is stronger than those of othertwo directions. In the model, the low-temperature physics is governed bydomain-wall excitations (defects) residing on bonds of the strong-couplingdirection. In this letter, we show that an additional small attractiveinteraction between defects (a ferromagnetic next-nearest-neighbor interactionin the weak-coupling direction) leads to a Berezinskii-Kosterlitz-Thouless(BKT) transition at a finite temperature, by performing the Monte Carlosimulation. The BKT phase can be viewed as the phase with a quasi long-rangeorder of defects. We determine the phase diagram in a wide parameter regime andargue the phase structure from statistical-mechanics and field-theoryviewpoints.

Quasi Long Range Order of Defects in Frustrated Antiferromagnetic Ising Models on Spatially Anisotropic Triangular Lattices