How do frustrations without disorder result in the spin-glass-like behavior of the kagomé antiferromagnet?

Abstract

Freezing of the classical spin liquid of the Heisenberg kagomé antiferromagnet is studied. At low temperature, the coplanar spin configurations are known to dominate among all possible three-dimensional low-energy states because of the fluctuation interaction. It is shown that the statistical weight of ${\bf q} =0$ domains is negligible. This allows one to describe coplanar states in terms of $\sqrt{3}\times \sqrt{3}$ domains with three possible spin orientations. The domain walls are mapped onto closed self-avoiding loops on the hexagonal lattice. The probability of domain formation is evaluated. It is shown that in FC (field cooled) regime a telescopic hierarchy of domains appears. The spatial and temporal behavior of the spin correlation function is estimated. The difference between FC and ZFC behavior is discussed.