The Kosterlitz-Thouless transition in the XY Kagom\'{e} antiferromagnet

TL;DR

This paper investigates the Kosterlitz-Thouless transition in the frustrated XY Kagome antiferromagnet, revealing unique decay behaviors of correlation functions and determining the transition temperature.

Contribution

It maps the frustrated Kagome system onto a ferromagnetic XY model on a hexagonal lattice and calculates the KT transition temperature.

Findings

Transition temperature is explicitly determined.

Spin correlation decays exponentially in low-temperature phase.

Order parameter correlation decays algebraically.

Abstract

The problem of the Kosterlitz-Thouless (KT) transition in the highly frustrated XY Kagom\'{e} antiferromagnet is solved. The problem is mapped onto that of the KT transition in the XY ferromagnet on the hexagonal lattice. The transition temperature is found. It is shown that the spin correlation function exponentially decays with distance even in the low-temperature phase, in contrast to the order parameter correlation function, which decays algebraically with distance.