Magnetic order of the two-dimensional antiferromagnetic 1/4-depleted square lattice

For a two-dimensional Heisenberg antiferromagnetic -depleted square lattice, it has been analytically proved that its ground state possesses simultaneously ferromagnetic and antiferromagnetic long-range orders, and exhibits ferrimagnetism. Numerical simulations of finite lattices using exact diagonalization show that the depletion strengthens the short-range spin-spin correlations whereas it weakens the long-range ones. The -depleted square lattice has a smaller susceptibility. This means that the geometric structure of the usual two-dimensional square lattice is more advantageous for establishing magnetic long-range order. By comparison of these two kinds of lattices, it is quite reliably inferred that Néel order exists in the ground state of the usual two-dimensional spin- Heisenberg antiferromagnetic square lattice.