One-dimensional XY antiferromagnetic Heisenberg model with nearest and next nearest neighbour exchange interactions

We study the one-dimensional anisotropic antiferromagnetic Heisenberg model with competing interactions using the self-consistent harmonic approximation. The dispersion relation, the correlation function and the susceptibility are obtained for several values of the ratio delta = J(2)/J(1) between the nearest (J(1)) and next nearest neighbour exchange interactions (J(2)). For delta < 0.25, the pair correlation function decays monotonically and exponentially to zero and the susceptibility has a maximum value at q = pi. For J(2) > 0.25 J(1), the exponential decay of the pair correlation is modified by an oscillatory behavior while the maximum of the susceptibility does not necessarily occur at q = pi. Furthermore, the phase diagram of a system with weakly coupled chains is considered. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.