We perform a real-space renormalization-group analysis for the two-dimensional antiferromagnetic Heisenberg model. We first derive an effective model, described by the Hamiltonian: H=J ${\mathcal{J}}_{\mathit{j}=1\mathrm{}}^{\mathit{L}}$ S(j)⋅S(j+1)+ ${\mathcal{J}}_{\mathit{j}=1\mathrm{}}^{\mathit{L}}$(-1${)}^{\mathit{j}}$‖J(j)‖S(0)⋅S(j), where S(0) represents a single spin located in the center of the ring. We show that the renormalized coupling constants ‖J(j)‖ tend to nonzero values as one increases the block size by successive renormalization. Using analytic and numerical arguments, we establish the existence of antiferromagnetic long-range order in the effective model and hence, in the original Heisenberg model. We compare our results with those obtained from perturbation theory, spin-wave theory, and exact-diagonalization calculations.

• Received 2 May 1994

DOI:https://doi.org/10.1103/PhysRevB.50.12702