Existence of Long-Range Magnetic Order in the Ground State of Two-Dimensional Spin-1/2 Heisenberg Antiferromagnets(Condensed Matter and Statistical Physics)

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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 even 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.
理論物理学刊行会の論文
2007-01-25