Spin-1/2 Heisenberg antiferromagnet on the square and triangular lattices: A comparison of finite temperature properties

Abstract

We compare and contrast the behavior of the spin-half Heisenberg antiferromagnet on the square and triangular lattices. For both models, high temperature expansions are obtained for the structure factor at the ordering vector, the correlation length, the uniform susceptibility, and the entropy. We show that the antiferromagnetic correlations are significantly larger for the square lattice than for the triangular lattice. Analysis of the structure factor and the correlation length shows that the spin stiffness is an order of magnitude smaller in the triangular lattice than in the square lattice. These results indicate that the triangular lattice, although weakly ordered at T=0, is close to a quantum critical point. Thus, in contrast to the square lattice, a semiclassical spin-wave picture may not be sufficient to describe the ground state.