Evidence for long-range order in the Heisenberg antiferromagnet on a triangular lattice

We present the results of effective-cluster calculations of the ground-state energy and average sublattice magnetization of the antiferromagnetic Heisenberg model on a triangular lattice. In these calculations the effective-cluster Hamiltonian consists of three contributions: the Hamiltonian of an isolated cluster with open boundary conditions, the effect of a variational field on the isolated cluster, and the intercluster energy. Extrapolation of the energy computed for clusters with 1, 3, 6, and 10 spins, leads to a ground-state energy ${\mathit{E}}_0$=-0.57J and an average sublattice magnetization 〈S〉=0.32.