Existence of long-range magnetic order in the ground state of two-dimensional spin-1/2 heisenberg antiferromagnets

We give a rigorous proof of the existence of long-range antiferromagnetic order in the ground state of several two-dimensional spin-1/2 Heisenberg systems. Three types of systems are considered. The first type consists of an number, N, of coupled square lattices with antiferromagnetic nearest-neighbor Heisenberg interactions. In this case, we prove the existence of long-range order (LRO) in the ground state for an interplane to inplane coupling ratio r in the range 0.16 ≤ r ≤ 2.1 for N ≥ 4. Further, we prove that the antiferromagnetic bilayer with ferromagnetic next-nearest-neighbor (nnn) interplane couplings possesses LRO in the ground state for 0.21 ≤ r < 1/4, where r is the absolute value of the ratio of the ferromagnetic and antiferromagnetic couplings. The final example consists of two antiferromagnetic spin-1/2 square lattices that are coupled via an antiferromagnetic nnn interplane coupling r. For r=1, this system is effectively a spin-1 square lattice and has an ordered ground state. We show that LRO exists in the region 0.85 ≤ r ≤ 1. (author)