Hidden long-range order in kagomé Heisenberg antiferromagnets

We give a physical picture of the low-energy sector of the spin-$\frac{1}{2}$ kagomé Heisenberg antiferromagnet (KAF). It is shown that the kagomé lattice can be presented as a set of stars which contain 12 spins and are arranged in a triangular lattice. Each of these stars has two degenerate singlet ground states which can be considered in terms of pseudospin. As a result of the interaction between stars we get the Hamiltonian of the Ising ferromagnet in a magnetic field. So in contrast to the common view there is a long-range order in KAF consisting of definite singlet states of stars.