The Kosterlitz-Thouless transition in the XY Kagomé antiferromagnet

The problem of the Kosterlitz-Thouless (KT) transition in the highly frustrated XY Kagomé 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. PACS numbers: 75.10.Hk, 75.30.H, 75.50.Ee, 74.50.+r Typeset using REVTEX 1 Generally, XY spins on two-dimensional lattices undergo a Kosterlitz-Thouless (KT) transition [1,2]. As a rule, physics of this transition does not depend on details of lattice structure. In the low temperature phase, pairs of spin direction singularities, vortices, with opposite topological charges form quasi-molecules. Above the transition temperature, the quasi-molecules decay into a vortex gas. In the low-temperature phase, the spin correlations decay algebraically with distance, above the transition temperature, they decay exponentially. Formally, the universality of the KT transition follows from the possibility to describe low-energy states of two-dimensional XY spin systems in terms of the nonlinear σ-model. The XY antiferromagnet on the two-dimensional Kagomé lattice is an exception from this class. It has infinitely many ground states, therefore its low-temperature properties cannot be described by the nonlinear σ-model. This makes the problem of a KT-like transition in the XY Kagomé antiferromagnet a special one, which is substantially more complicated than the standard theory of the KT transition. The very possibility of a KT transition in such an unusual system is under question. The problem of the KT transition in the Kagomé antiferromagnet was first addressed by Huse and Rutenberg [3]. They suggested that the order parameter for the KT transition is e where θ is the angle of a spin. This order parameter is invariant with respect to any arbitrary choice of ground states, which are a subset of local 2π/3 spin rotations. Therefore this order parameter can change smoothly in the plane even though spins rotate locally at multiple 2π/3 angles. An indirect evidence of the KT transition in the Kagomé antiferromagnet was obtained from MC simulation [4]. A network of Josephson junctions with the π-phase shift can be mapped onto the antiferromagnetic XY model as well. Experimental studies of artificial networks of Josephson junctions on the Kagomé lattice make this problem especially appealing [5]. In this paper, we examine the KT-like transition in the XY Kagomé antiferromagnet. We find that the KT transition in the Kagomé antiferromagnet does exist, we evaluate the transition temperature, and we show that the spin correlation function behaves itself in an unusual way. 2