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

TL;DR

This paper demonstrates that adding a small attractive interaction between defects in a frustrated antiferromagnetic Ising model on anisotropic triangular lattices induces a BKT transition, leading to a phase with quasi long-range order.

Contribution

It reveals that a ferromagnetic next-nearest-neighbor interaction causes a BKT transition in the model, which was previously understood to have no phase transition at zero temperature.

Findings

Identification of a BKT transition induced by defect interactions

Phase diagram mapping in parameter space

Evidence of quasi long-range order of defects

Abstract

It is known that there is no phase transition down to zero temperature in the antiferromagnetic Ising model on spatially anisotropic triangular lattices, in which the exchange coupling of one direction is stronger than those of other two directions. In the model, the low-temperature physics is governed by domain-wall excitations (defects) residing on bonds of the strong-coupling direction. In this letter, we show that an additional small attractive interaction between defects (a ferromagnetic next-nearest-neighbor interaction in the weak-coupling direction) leads to a Berezinskii-Kosterlitz-Thouless (BKT) transition at a finite temperature, by performing the Monte Carlo simulation. The BKT phase can be viewed as the phase with a quasi long-range order of defects. We determine the phase diagram in a wide parameter regime and argue the phase structure from statistical-mechanics and field-theory viewpoints.