Abstract

An analytic solution for the Heisenberg Hamiltonian with arbitrarily long-range, ferromagnetic and/or antiferromagnetic, interactions on a Bethe lattice is obtained in the semiclassical approximation (S --> infinity). The density of states of the excitations is evaluated in the one-spin-wave approximation. The stability of a general helical ground state configuration, against variations in the magnitude and sign of the long-range interactions, is investigated for several illustrative examples, generating a wealth of sharp and smooth parametric transitions.