Ground-State Long-Range Order in the Two-Dimensional XXZ Model

Abstract

We prove the existence of Néel-type long-range order in the ground state of the spin-1⁄2 XXZ model with Δ(exchange anisotropy)>1.67 on the square lattice. We further show the existence of long-range order for Δ>1.10 and 0≤Δ<0.59 by assuming monotonicity of nearest neighbor correlations as functions of the system size. The assumption of monotonicity is supported by numerical calculations.